SOLUTION: Could you please show me how to prove the following identities...
A) cos2x=2cos^2x-1
B) cos2x=1-2sin^2x
C) (1/1+sinx)+(1/1-sinx)=2sec^2x
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Question 906155: Could you please show me how to prove the following identities...
A) cos2x=2cos^2x-1
B) cos2x=1-2sin^2x
C) (1/1+sinx)+(1/1-sinx)=2sec^2x
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
prove the following identities...
A) cos2x=2cos^2x-1
start with left side:
cos2x=cos(x+x)
=coscosx-sinxsinx
=cos^2x-(1-cos^2x)=2cos^x-1
verified: left side=right side
..
B) cos2x=1-2sin^2x
start with left side:
cos2x=cos(x+x)
=coscosx-sinxsinx
=cos^2x-sin^2x=1-sin^2x-sin^2x
=1-2sin^2x
verified: left side=right side
..
C) (1/1+sinx)+(1/1-sinx)=2sec^2x
start with left side:
(1/1+sinx)+(1/1-sinx)
=(1-sinx+1+sinx)/(1+sinx)(1-sinx)
=2/1-sin^2x
=2/cos^2x
=2sec^2x
verified: left side=right side
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