Find the exact value of cos(sin^−1 2𝑥)

Question

the 2x is not raised to the power of sin

Answer 1

cos(sin^-1 2x) = 1-4x^2

sinA = 2x = opposite side over hypotenuse = 2x/1

2x = opposite side, sqr(1-4x^2) = adjacent side

A= sin^-1 2x

cosA = adjacent side/hypotenuse = square root of [1 -(2x)^2]/1 = sqr(1-4x^2)/1=

= sqr(1-4x^2)