Question #88933
If tan^2a=1+2tan^2b,then prove that cos 2b=1+2cos2a
1
Expert's answer
2019-05-02T10:11:20-0400

The identity: tan2a = 1cos2a\frac{1}{cos^{2}a} - 1; tan2b = 1cos2b\frac{1}{cos^{2}b} - 1;

    \implies 1cos2a\frac{1}{cos^{2}a} - 1 = 1 + 2(1cos2b\frac{1}{cos^{2}b} - 1);

    \implies 1cos2a\frac{1}{cos^{2}a} = 2cos2b\frac{2}{cos^{2}b} ; cos2b = 2cos2a;

The identity: cos2b = 1+cos2b2\frac{1+cos2b}{2}; cos2a = 1+cos2a2\frac{1+cos2a}{2} ;

    \implies 1+cos2b2\frac{1+cos2b}{2} = 1 + cos2a;

    \implies cos2b = 1 + 2cos2a.

Answer: from the relation tan2a = 1 + 2tan2b, follows: cos2b = 1 + 2cos2a.



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS