Prove this is an identity? 1-sinx=1-sin²(-x)/1-sin(-x)

2 Answers
Mar 31, 2018

See below.

Explanation:

Get rid of sin(-x). Recall that sin(-x)=-sinx.

1-sinx=(1-sin^2x)/(1-(-sinx))

1-sinx=(1-sin^2x)/(1+sinx)

Now, from the difference of squares, we know that 1-sin^2x=(1+sinx)(1-sinx):

1-sinx=(cancel(1+sinx)(1-sinx))/(cancel(1+sinx))

1-sinx=1-sinx

So, this is indeed an identity.

Mar 31, 2018

Look below

Explanation:

First, let's look at the numerator on the right side of the equation. sin(-x)=-sin(x), so sin^2(-x)=(-sin(x))^2=sin^2(x), so the numerator is 1-sin^2(x) Looking at the denominator, you'll see that it is equal to 1+sin(x). Dividing the numerator and denominator, you'll see that the identity is true.