The directions say to prove the identity. I understand how these two functions work, but I don't understand how to go through the process of getting from the left side to the right side.

Could you remind me how you factored out sin^2x from the left in proof step 5? Other than that, everything else was very helpful, it makes so much more sense.

Angel's answer is generally correct, if a bit confusing. I would have said it this way: think of (sin^{2}x - sin^{2}x cos^{2}x) as (a - ab) where a=sin^{2}x and b=cos^{2}x. Now, when 'factoring out' we are looking for an expression that is common in both terms 'a' and 'ab'. The common term is simply 'a', so we can factor it out. Factoring it out is the opposite of the 'distribution' property - that is, it is distribution in reverse. So for each term, we can ask "a times what is equal to the term?" So for the first term, a, we say "a times what is equal to a?" and the answer is 1. For the second term, "a times what is equal to ab?" and the answer is b. So: (a - ab) = a(1 - b).

Now since we said a=sin2x and b=cos^{2}x, we know that:

Fallou, there are two additive terms on the left: sin^{2}x/cos^{2}x and sin^{2}x. We need the second term, sin^{2}x to have a common denominator of cos^{2}x, so we multiply both the numerator (sin^{2}x) and denominator (an implicit 1) by cos^{2}x, resulting in:

## Comments

Could you remind me how you factored out sin^2x from the left in proof step 5? Other than that, everything else was very helpful, it makes so much more sense.

look at (sin^2(x)-sin^2(x)cos^2(x)) as (2-2x). Both terms have a two therefore can be factored out, 2(1-x).

Angel's answer is generally correct, if a bit confusing. I would have said it this way: think of (sin

^{2}x - sin^{2}x cos^{2}x) as (a - ab) where a=sin^{2}x and b=cos^{2}x. Now, when 'factoring out' we are looking for an expression that is common in both terms 'a' and 'ab'. The common term is simply 'a', so we can factor it out. Factoring it out is the opposite of the 'distribution' property - that is, it is distribution in reverse. So for each term, we can ask "a times what is equal to the term?" So for the first term, a, we say "a times what is equal to a?" and the answer is 1. For the second term, "a times what is equal to ab?" and the answer is b. So: (a - ab) = a(1 - b).Now since we said a=sin2x and b=cos

^{2}x, we know that:sin

^{2}x - sin^{2}x cos^{2}x = sin^{2}x (1 - cos^{2}x)^{2}x/cos^{2}x and sin^{2}x. We need the second term, sin^{2}x to have a common denominator of cos^{2}x, so we multiply both the numerator (sin^{2}x) and denominator (an implicit 1) by cos^{2}x, resulting in:^{2}x sin^{2}x cos^{2}x^{2}x cos^{2}x^{2}x - sin^{2}x cos^{2}x^{2}x