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Answer is-1/3
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Answer:
This is the answer . Hope it will help you .
Answer- The above question is from the chapter 'Introduction to Trigonometry'.
Trigonometry- The branch of Mathematics which helps in dealing with measure of three sides of a right-angled triangle is called Trigonometry.
Trigonometric Ratios:
sin θ = Perpendicular/Hypotenuse
cos θ = Base/Hypotenuse
tan θ = Perpendicular/Base
cosec θ = Hypotenuse/Perpendicular
sec θ = Hypotenuse/Base
cot θ = Base/Perpendicular
Also, tan θ = sin θ/cos θ and cot θ = cos θ/sinθ
Trigonometric Identites:
1. sin²θ + cos²θ = 1
2. sec²θ - tan²θ = 1
3. cosec²θ - cot²θ = 1
Given question: If sin A = √3/2, find the value of 2cot²A - 1.
Solution: In a Δ, sin A = √3/2
Perpendicular/Hypotenuse = √3/2
Let P = √3k and H = 2k.
By Pythagoras Theorem, P² + B² = H²
(√3k)² + B² = (2k)²
3k² + B² = 4k²
B² = k²
⇒ B = 1k
We know that cot A = Base/Perpendicular = k/√3k
cot A = 1/√3
Now, 2 cot²A - 1
= 2 × (1/√3)² - 1
= 2/3 - 1
= (2-3)/3
= -1/3