Question

If cos 2 A-sin 2 A=tan 2 A, proove that cosA=1/root2 cosA

Answer 1

cos^2 A - (1- cos^2 A) = sec ^2 A -1

[ since sin ^2 A = 1- cos^2 A and tan^2 A = sec ^2 A -1 ]

cos^2 A - 1 + cos ^2 A = 1/ cos ^2 A -1

[ since sec ^2 A = 1/ cos ^2 A]

2 cos ^2 A = 1/ cos ^2 A - 1 + 1

2 cos ^2 A = 1/ cos^2 A

do the squre root for both sides

root 2* cos A = 1/ cos A

therefore

cos A = 1/( root 2* cos A)