SOLUTION: Please Prove the following identities 1.) Tan (x/2) = tan (x)/sec (x) + 1 2.) sin(2x) - tan(x) = tan(x) cos (2x)

Algebra ->  Trigonometry-basics -> SOLUTION: Please Prove the following identities 1.) Tan (x/2) = tan (x)/sec (x) + 1 2.) sin(2x) - tan(x) = tan(x) cos (2x)       Log On


   

Question 816297: Please Prove the following identities
1.) Tan (x/2) = tan (x)/sec (x) + 1
2.) sin(2x) - tan(x) = tan(x) cos (2x)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Please Prove the following identities
1.) Tan (x/2) = tan (x)/sec (x) + 1
start with right side:
tanx/(secx+1)=(sin/cos)/((1/cos)+1)=(sin/cos)/((1+cos)/cos)
=sin%28x%29%2F%281%2Bcos%28x%29%29=tan%28x%2F2%29
verified: right side=left side
..
2.) sin(2x) - tan(x) = tan(x) cos (2x)
start with right side:
tanxcos2x=(sin/cos)(2cos^2-1)=2sincos-sin/cos=sin(2x)-tan(x)
verified: right side=left side