Register to reply

Proving Trig Ident.

by Miike012
Tags: ident, proving, trig
Share this thread:
Miike012
#1
Mar19-11, 02:09 PM
P: 1,011
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???
Phys.Org News Partner Science news on Phys.org
Scientists discover RNA modifications in some unexpected places
Scientists discover tropical tree microbiome in Panama
'Squid skin' metamaterials project yields vivid color display
jhae2.718
#2
Mar19-11, 02:13 PM
PF Gold
jhae2.718's Avatar
P: 1,160
[tex]\cos(2s) \equiv \cos^2(s) - \sin^2(s)[/tex]
Miike012
#3
Mar19-11, 02:18 PM
P: 1,011
Yes that is true... but then why isnt the expression
2*sin(2s)*(cos^2 - Sin^2)4
?

jhae2.718
#4
Mar19-11, 02:23 PM
PF Gold
jhae2.718's Avatar
P: 1,160
Proving Trig Ident.

What they did was:
[tex]\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}[/tex]

which is simply substituting in [tex]2\sin(s)\cos(s)[/tex] for [tex]\sin(2s)[/tex], and [tex]\cos^2(s)-\sin^2(s)[/tex] for [tex]\cos(2s)[/tex].
Miike012
#5
Mar19-11, 02:25 PM
P: 1,011
Thank you!
jhae2.718
#6
Mar19-11, 02:27 PM
PF Gold
jhae2.718's Avatar
P: 1,160
Glad to help!


Register to reply

Related Discussions
Simplifying trig Ident. Help Precalculus Mathematics Homework 16
Proving Trig ID Precalculus Mathematics Homework 4
More proving trig identities Precalculus Mathematics Homework 3
Proving trig identities! Introductory Physics Homework 1
Homework Help with trig ident... Precalculus Mathematics Homework 3