# How do you simplify #sin(2cos^-1(4/5))#?

##### 1 Answer

Nov 15, 2017

Use the identity

Then use the identity

#### Explanation:

Given:

Use the identity

The cosine of its inverse yields its argument:

Perform the multiplication:

Use the identity #sin(A) = +-sqrt(1-cos^2(A))

Again, the cosine of its inverse yields its argument:

To determine whether to choose the positive or negative value, one would need know whether the angle was in the first or fourth quadrant.