Question

Use Pythagorean identities to rewrite each of the following trigonometric expressions.

${\sin }^{2}x=\_\_\_\_\_\_\_$

Short answer

The obtained result is$1-{\cos }^{2}x$.

Step-by-step solution

Step 1. Given information.

Consider the given expression.

${\sin }^{2}x$

Step 2. Apply the Pythagorean identities to rewrite the expression.

The Pythagorean identity is defined as,

${\sin }^{2}x+{\cos }^{2}x=1$

Rewrite the above identity,

${\sin }^{2}x=1-{\cos }^{2}x$