Question

If possible, verify sin^2(x)/1 + cos(x) = 1 - cos(x) by rewriting the left hand side of the equation.

I really really don't understand identities, and I'm not getting replies from my teacher. Thank you for any help I do get!!​

Answer 1

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

We know that sin^2 x = 1 - cos^2 x. It is one of our trig identities.

We now have this:

(1 - cos^2 x)/(1 + cos x) = 1 - cos x

Take note:

1 - cos^2 x is a perfect square difference in terms of cosine.

So, (1 - cos^2 x) = (1 + cos x)(1 - cos x).

We now have this:

[(1 + cos x)(1 - cos x)]/(1 + cos x) = 1 - cos x

Do you see what happens on theft side?

On the left side, (1 + cos x) cancels out on the top and bottom.

We are now left with this:

1 - cos x = 1 - cos x

Done!!