Question

find the value of sin(1/2cot^-1(8/15) ) ​

Answer 1

answer : sin(1/2cot^-1(8/15) ) = 3/√34

we have to find the value of sin(1/2 cot-¹(8/15))

let 1/2 cot-¹(8/15) = θ

⇒cot-¹(8/15) = 2θ

⇒8/15 = cot2θ

⇒tan2θ = 15/8

⇒2tanθ/(1 - tan²θ) = 15/8

⇒16tanθ = 15 - 15 tan²θ

⇒15 tan²θ + 16tanθ - 15 = 9

⇒tanθ = -5/3 , 3/5

when we take tanθ = 3/5 ⇒sinθ = 3/√34

θ = sin-¹(3/√34)

⇒1/2 cot-¹(8/15) = sin-¹(3√34)

sin(1/2 cot-¹(8/15) = sin(sin-¹(3√34) = 3/√34

also read similar questions : If sin A = √3/2, find the value of 2cot^2A-1

https://brainly.in/question/6332482

if sin theta =1/3 then find the value of 2cot^2 theta +2

https://brainly.in/question/2358019