# `cos(arcsin(2x))` Write an algebraic expression that is equivalent to the given expression. (Hint: Sketch a right triangle.)

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### 2 Answers

`cos(sin^(-1)(2x)) = cos(cos^(-1)(sqrt(1-(2x)^2)))`

`=cos(cos^(-1)(sqrt(1-4x^2)))`

`=sqrt(1-4x^2)`

`cos(arcsin(2x))`

let `theta = arcsin(2x)`

so we need to find `cos(theta)`

As ` theta = arcsin(2x)`

`sin(theta)= 2x = (2x)/1 = (opposite side) / (hypotenuse)`

by using the right triangle we get the hypotenuse as =1

so, the adjacent side = sqrt(hypotenuse ^2 - opposite side^2)

`= sqrt(1-(2x)^2)`

=sqrt(1-4x^2)

so` cos(theta)` = adjacent side/hypotenuse = `sqrt(1-4x^2)/1`