SOLUTION: verify each of the following identities. pls. help me solve this problem.. thank you in advance 1. 1+cos theta=(tan^2theta)/(1-sec theta + tan^2theta) 2. cos 3x = cos^3x-3s

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Question 421167: verify each of the following identities.
pls. help me solve this problem.. thank you in advance

1. 1+cos theta=(tan^2theta)/(1-sec theta + tan^2theta)
2. cos 3x = cos^3x-3sin^2x cos x
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
1. 1+cos theta=(tan^2theta)/(1-sec theta + tan^2theta)
2. cos 3x = cos^3x-3sin^2x cos x
..
1.1+cos=tan^2/1-sec+tan^2
Starting with right-hand side,
tan^2/1-sec+tan^2
using identity:(tan^2x+1=sec^2x)
sec^2-1/1-sec+sec^2-1
=(sec+1)(sec-1)/sec^2-sec
=(sec+1)(sec-1)/sec(sec-1)
=(sec+1)/sec
=(sec/sec)+(1/sec)
=1+cos
verified:
left-hand side = right hand side
..
2.cos3x=cos^3x-3sin^2xcosx
Starting with left-hand side
Using identity:(cos(x+y)=cosxcosy-sinxsiny)
cos3x=cos(x+2x)=cosxcos2x-sinxsin2x
Using identities:(Cos2x and sin2x)
=cosx(cos^2x-sin^2x)-sinx(2sinxcosx)
=cos^3x-sin^2xcosx-2sin^2cosx
=cos^3x-3sin^2cosx
verified:
left-hand side=right-hand side