Question

Verify the Identity? Sinx / 1-cos^2x = cscx

Answer 1

To solve this, we need to use the Pythagorean Trig Identity.

Explanation:

The Pythagorean Identity states:

`cos^2x + sin^2x = 1`

We manipulate this to get either `cos^2x` or `sin^2x` by itself. For this problem, we want `sin^2x` by itself. To do this, we can simply subtract the `cos^2x` over to the other side, making it:

`sin^2x = 1-cos^2x`

Knowing this, we can verify the trigonometric equation. Since we now know that `1-cos^2x` equals `sin^2x`, we can substitute that in, giving us:

`sinx / sin^2x = cscx`

From here, we can do a simple cancellation of a `sinx` in the numerator and denominator, which leaves us with:

`1 / sinx = cscx`

And then:

`cscx = cscx`