Class 10 Exam > Class 10 Questions > If ( 1 sin²A ) = 3sinAcosA then prove that ...
Start Learning for Free
If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2?
Verified Answer
If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2?
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2?
Given:
(1 + sin²A) = 3sinAcosA
To prove:
tanA = 1 or 1/2
Proof:
Simplifying the given equation:
(1 + sin²A) = 3sinAcosA
1 + sin²A = 3sinAcosA
sin²A + 1 = 3sinAcosA
sin²A + cos²A = 3sinAcosA
1 = 3sinAcosA
Using trigonometric identity:
sin²A + cos²A = 1
Comparing the above equation with the simplified equation:
sin²A + cos²A = 3sinAcosA
Equating the coefficients:
1 = 3sinAcosA
Dividing both sides by cosA:
secA = 3sinA
Dividing both sides by sinA:
tanA = 3
Therefore, tanA = 3.
Now, we need to find the possible values of A for which tanA = 3.
Solving for A:
tanA = 3
A = tan⁻¹(3)
Using a calculator, we find:
A ≈ 71.57 degrees
Therefore, one possible value of A is approximately 71.57 degrees.
Now, we need to find the other possible value of A.
Using the periodicity of the tangent function:
tan(A + 180 degrees) = tanA
Therefore, the other possible value of A is:
A + 180 degrees ≈ 71.57 + 180 degrees
A + 180 degrees ≈ 251.57 degrees
Therefore, the possible values of A are approximately 71.57 degrees and 251.57 degrees.
Now, we need to find tanA for these values of A:
tan(71.57 degrees) ≈ 3
tan(251.57 degrees) ≈ 3
Therefore, the possible values of A for which tanA = 3 are approximately 71.57 degrees and 251.57 degrees.
However, we need to find the values of A for which tanA = 1 or 1/2.
Now, we need to find the possible values of A for which tanA = 1 or 1/2.
Solving for A when tanA = 1:
A = tan⁻¹(1
|
|
Explore Courses for Class 10 exam
|
|
Top Courses for Class 10View all
Question Description
If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2?.
If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2?.
Solutions for If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2? 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 If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2? defined & explained in the simplest way possible. Besides giving the explanation of
If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2?, a detailed solution for If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2? has been provided alongside types of If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2? theory, EduRev gives you an
ample number of questions to practice If ( 1 sin²A ) = 3sinAcosA then prove that tanA = 1 or 1/2? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily