# Proving Trig Ident.

by Miike012
Tags: ident, proving, trig
 P: 976 1. The problem statement, all variables and given/known data sin(4s)/4 = cos^3(s)*Sin(s) - sin^3(s)*cos(s) In the book they did.... 2*sin(2s)*cos(2s)/4 = 2*2*sin(s)*cos(s)/4 *(cos^2(s) - sin^2(s)) (I understand everything up until they multiplyed the 2*2*sin(s)*cos(s)/4 expression by cos^2(s) - sin^2(s)... where did cos^2(s) - sin^2(s) come from???
 PF Patron P: 1,132 $$\cos(2s) \equiv \cos^2(s) - \sin^2(s)$$
 P: 976 Yes that is true... but then why isnt the expression 2*sin(2s)*(cos^2 - Sin^2)4 ?
PF Patron
P: 1,132

## Proving Trig Ident.

What they did was:
$$\frac{2\sin(2s)\cos(2s)}{4} = \frac{2\cdot \left(2\sin(s)\cos(s)\right)\left(\cos^2(s) - \sin^2(s)\right)}{4}$$

which is simply substituting in $$2\sin(s)\cos(s)$$ for $$\sin(2s)$$, and $$\cos^2(s)-\sin^2(s)$$ for $$\cos(2s)$$.
 P: 976 Thank you!
 PF Patron P: 1,132 Glad to help!

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