Verify the identity.

Question

anonymous · Answer

attachment

anonymous · Answer

I figured that it was an identity

mathslover · Answer

OK try to do cross multiplication

mathslover · Answer

(1-sin x)(1+sin x) = cos x * cos x

What do you get?

luigi0210 · Answer

Uh, mathsolver you can't cross multiply when verifying an identity

whpalmer4 · Answer

@Luigi0210 Of course you can!

hero · Answer

I don't see anything wrong with cross multiplying to verify the identity

whpalmer4 · Answer

Cross multiplication is just multiplying both sides by both denominators.

hero · Answer

Teachers have unnecessary disputes about methods used to verify identities.

luigi0210 · Answer

Yes, but you're trying to prove that both sides are the same. Cross multiplication doesn't mean you are proving it. You are just assuming that they are equal to each other.

hero · Answer

And there's no problem with that. You do the same thing when you're dealing with algebraic proportions. When you solve algebraic proportions, you are not sure whether they are equal either until you solve it. When dealing with trigonometric proprortions, you'll find out whether or not they are equal once you cross multiply and simplify the expression on both sides.

whpalmer4 · Answer

If they aren't equal, you'll end up with a result that can't have an equal sign in the middle, such as $$2=0$$

hero · Answer

^exactly

hero · Answer

But if they are equal, you might end up with something like 

1 = 1

which would verify their equality.