129k views
0 votes
Prove that : Cos 2A =cot^2-1/cot^2+1​

User Gerbus
by
8.1k points

1 Answer

3 votes

Answer:


\cos(2A) = { \cos }^(2) A - { \sin }^(2) A \\ = { \cos }^(2) A - \frac{1}{ \csc {}^(2) A} \\ \\ = \frac{( { \cos}^(2) A. \csc {}^(2)A ) - 1}{ { \csc }^(2) A} \\ \\ = \frac{( \frac{ { \cos}^(2)A }{ { \sin }^(2) A}) - 1 }{ { \csc }^(2) A} \\ \\ = \frac{ { \cot}^(2)A - 1 }{ { \csc}^(2) A}

but csc²A = cot²A + 1:


= \frac{ { \cot}^(2)A - 1 }{ { \cot }^(2)A + 1 }

# proved

User Roy Van Zanten
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories