All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
Class 10 Exam  >  Class 10 Questions  >  State whether the following are true or false... Start Learning for Free
SaveJoin the Discussion on the App
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?
Clear all your Class 10 doubts with EduRev
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.
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.
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

Similar Class 10 Doubts

Read the given passage and answer the questions:Metallic Character: The ability of an atom to donate electrons and form positive ions (cation) is known as electro-positivity or metallic character. Down the group, metallic character increases due to increase in atomic size and across the period, from left to right electropositivity decreases due to decrease in atomic size.Non-Metallic Character: The ability of an atom to accept electrons to form a negative ion (anion) is called non-metallic character or electronegativity. The elements having high electro-negativity have a higher tendency to gain electrons and form anion. Down the group, electronegativity decreases due to increase in atomic size and across the period, from left to right electro -negativity increases due to decrease in atomic size.Which of the following reasons correctly justifies that “Fluorine (72pm) has a smaller atomic radius than Lithium (152pm)”?

Read the given passage and answer the questions:Metallic Character: The ability of an atom to donate electrons and form positive ions (cation) is known as electro-positivity or metallic character. Down the group, metallic character increases due to increase in atomic size and across the period, from left to right electropositivity decreases due to decrease in atomic size. Non-Metallic Character: The ability of an atom to accept electrons to form a negative ion (anion) is called non-metallic character or electronegativity. The elements having high electro-negativity have a higher tendency to gain electrons and form anion. Down the group, electronegativity decreases due to increase in atomic size and across the period, from left to right electro -negativity increases due to decrease in atomic size.Which of the following has highest electronegativity?

Read the given passage and answer the questions:Metallic Character: The ability of an atom to donate electrons and form positive ions (cation) is known as electro-positivity or metallic character. Down the group, metallic character increases due to increase in atomic size and across the period, from left to right electropositivity decreases due to decrease in atomic size. Non-Metallic Character: The ability of an atom to accept electrons to form a negative ion (anion) is called non-metallic character or electronegativity. The elements having high electro-negativity have a higher tendency to gain electrons and form anion. Down the group, electronegativity decreases due to increase in atomic size and across the period, from left to right electro -negativity increases due to decrease in atomic size.Identify the reason for the gradual change in electronegativity in halogens down the group.

Top Courses for Class 10View all

Top Courses for Class 10

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?.
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

Top Courses for Class 10

Explore Courses

Suggested Free Tests

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© 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