Class 10 Exam > Class 10 Questions > State whether the following are true or false...
Start Learning for Free
State whether the following are true or false. Justify your answer.
(i) sin(A + B) = sin A + sin B
(ii) The value of sin theta increases as e increases.
(iii) The value of cos theta increases as e increases.
(iv) sin theta = cos theta for all values of 0.
(v) cot A is not defined for A = 0?
(i) sin(A + B) = sin A + sin B
(ii) The value of sin theta increases as e increases.
(iii) The value of cos theta increases as e increases.
(iv) sin theta = cos theta for all values of 0.
(v) cot A is not defined for A = 0?
Most Upvoted Answer
State whether the following are true or false. Justify your answer.(i)...
Statement (i): sin(A + B) = sin A + sin B
- False: The correct formula is sin(A + B) = sin A * cos B + cos A * sin B. The addition of angles involves both sine and cosine terms, not just the sine values.
Statement (ii): The value of sin theta increases as e increases
- False: The sine function oscillates between -1 and 1 and is periodic with a period of 2π. The value of sin theta does not depend on 'e' (Euler's number) but rather on the angle theta itself. As theta increases, sin theta will increase or decrease depending on the angle.
Statement (iii): The value of cos theta increases as e increases
- False: Similar to the sine function, the cosine function also oscillates and does not depend on 'e'. The value of cos theta varies based on the angle theta, not on any external factor like 'e'.
Statement (iv): sin theta = cos theta for all values of 0
- False: sin theta = cos theta only at specific angles, namely 45 degrees (π/4 radians) and angles coterminal with it. For most angles, sine and cosine will yield different values.
Statement (v): cot A is not defined for A = 0
- True: Cotangent is defined as cos A/sin A. When A = 0, sin A = 0, leading to division by zero, which is undefined. Therefore, cot A is indeed not defined for A = 0.
- False: The correct formula is sin(A + B) = sin A * cos B + cos A * sin B. The addition of angles involves both sine and cosine terms, not just the sine values.
Statement (ii): The value of sin theta increases as e increases
- False: The sine function oscillates between -1 and 1 and is periodic with a period of 2π. The value of sin theta does not depend on 'e' (Euler's number) but rather on the angle theta itself. As theta increases, sin theta will increase or decrease depending on the angle.
Statement (iii): The value of cos theta increases as e increases
- False: Similar to the sine function, the cosine function also oscillates and does not depend on 'e'. The value of cos theta varies based on the angle theta, not on any external factor like 'e'.
Statement (iv): sin theta = cos theta for all values of 0
- False: sin theta = cos theta only at specific angles, namely 45 degrees (π/4 radians) and angles coterminal with it. For most angles, sine and cosine will yield different values.
Statement (v): cot A is not defined for A = 0
- True: Cotangent is defined as cos A/sin A. When A = 0, sin A = 0, leading to division by zero, which is undefined. Therefore, cot A is indeed not defined for A = 0.
Community Answer
State whether the following are true or false. Justify your answer.(i)...
Statement (i): sin(A + B) = sin A + sin B
- False: This statement is incorrect. The correct formula is sin(A + B) = sin A * cos B + cos A * sin B. The sine function does not simply add the sine of two angles.
Statement (ii): The value of sin theta increases as e increases
- False: The value of sin theta depends on the angle theta, not on e (Euler's number). As theta increases from 0 to 90 degrees, sin theta increases, but this is independent of the value of e.
Statement (iii): The value of cos theta increases as e increases
- False: Similar to the previous statement, cos theta is a function of the angle theta alone. It decreases as theta increases from 0 to 90 degrees, regardless of the value of e.
Statement (iv): sin theta = cos theta for all values of 0
- False: Sin theta equals cos theta only at specific angles, such as 45 degrees (or π/4 radians). For all other values, this equality does not hold.
Statement (v): cot A is not defined for A = 0
- True: Cotangent is defined as cot A = cos A/sin A. At A = 0, sin 0 = 0, making cot A undefined since division by zero is not possible. Thus, cot 0 is indeed not defined.
- False: This statement is incorrect. The correct formula is sin(A + B) = sin A * cos B + cos A * sin B. The sine function does not simply add the sine of two angles.
Statement (ii): The value of sin theta increases as e increases
- False: The value of sin theta depends on the angle theta, not on e (Euler's number). As theta increases from 0 to 90 degrees, sin theta increases, but this is independent of the value of e.
Statement (iii): The value of cos theta increases as e increases
- False: Similar to the previous statement, cos theta is a function of the angle theta alone. It decreases as theta increases from 0 to 90 degrees, regardless of the value of e.
Statement (iv): sin theta = cos theta for all values of 0
- False: Sin theta equals cos theta only at specific angles, such as 45 degrees (or π/4 radians). For all other values, this equality does not hold.
Statement (v): cot A is not defined for A = 0
- True: Cotangent is defined as cot A = cos A/sin A. At A = 0, sin 0 = 0, making cot A undefined since division by zero is not possible. Thus, cot 0 is indeed not defined.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Top Courses for Class 10View all
State whether the following are true or false. Justify your answer.(i) sin(A + B) = sin A + sin B(ii) The value of sin theta increases as e increases. (iii) The value of cos theta increases as e increases. (iv) sin theta = cos theta for all values of 0. (v) cot A is not defined for A = 0?
Question Description
State whether the following are true or false. Justify your answer.(i) sin(A + B) = sin A + sin B(ii) The value of sin theta increases as e increases. (iii) The value of cos theta increases as e increases. (iv) sin theta = cos theta for all values of 0. (v) cot A is not defined for A = 0? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about State whether the following are true or false. Justify your answer.(i) sin(A + B) = sin A + sin B(ii) The value of sin theta increases as e increases. (iii) The value of cos theta increases as e increases. (iv) sin theta = cos theta for all values of 0. (v) cot A is not defined for A = 0? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for State whether the following are true or false. Justify your answer.(i) sin(A + B) = sin A + sin B(ii) The value of sin theta increases as e increases. (iii) The value of cos theta increases as e increases. (iv) sin theta = cos theta for all values of 0. (v) cot A is not defined for A = 0?.
State whether the following are true or false. Justify your answer.(i) sin(A + B) = sin A + sin B(ii) The value of sin theta increases as e increases. (iii) The value of cos theta increases as e increases. (iv) sin theta = cos theta for all values of 0. (v) cot A is not defined for A = 0? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about State whether the following are true or false. Justify your answer.(i) sin(A + B) = sin A + sin B(ii) The value of sin theta increases as e increases. (iii) The value of cos theta increases as e increases. (iv) sin theta = cos theta for all values of 0. (v) cot A is not defined for A = 0? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for State whether the following are true or false. Justify your answer.(i) sin(A + B) = sin A + sin B(ii) The value of sin theta increases as e increases. (iii) The value of cos theta increases as e increases. (iv) sin theta = cos theta for all values of 0. (v) cot A is not defined for A = 0?.
Solutions for State whether the following are true or false. Justify your answer.(i) sin(A + B) = sin A + sin B(ii) The value of sin theta increases as e increases. (iii) The value of cos theta increases as e increases. (iv) sin theta = cos theta for all values of 0. (v) cot A is not defined for A = 0? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of State whether the following are true or false. Justify your answer.(i) sin(A + B) = sin A + sin B(ii) The value of sin theta increases as e increases. (iii) The value of cos theta increases as e increases. (iv) sin theta = cos theta for all values of 0. (v) cot A is not defined for A = 0? defined & explained in the simplest way possible. Besides giving the explanation of
State whether the following are true or false. Justify your answer.(i) sin(A + B) = sin A + sin B(ii) The value of sin theta increases as e increases. (iii) The value of cos theta increases as e increases. (iv) sin theta = cos theta for all values of 0. (v) cot A is not defined for A = 0?, a detailed solution for State whether the following are true or false. Justify your answer.(i) sin(A + B) = sin A + sin B(ii) The value of sin theta increases as e increases. (iii) The value of cos theta increases as e increases. (iv) sin theta = cos theta for all values of 0. (v) cot A is not defined for A = 0? has been provided alongside types of State whether the following are true or false. Justify your answer.(i) sin(A + B) = sin A + sin B(ii) The value of sin theta increases as e increases. (iii) The value of cos theta increases as e increases. (iv) sin theta = cos theta for all values of 0. (v) cot A is not defined for A = 0? theory, EduRev gives you an
ample number of questions to practice State whether the following are true or false. Justify your answer.(i) sin(A + B) = sin A + sin B(ii) The value of sin theta increases as e increases. (iii) The value of cos theta increases as e increases. (iv) sin theta = cos theta for all values of 0. (v) cot A is not defined for A = 0? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup