12 If tane = 2-1, then prove that sin ecose 4

If sin A + sin^(2)A + sin^(3)A =1 , then , prove that cos^(6) A - 4 cos^(4) A + 8 cos^(2) A =4 .

If cos A+cos B=1/2 and sin A +sin B=1/4 then prove that tan ((A+B)/2)=1/2 .

If1+ sin^@0 = 3sino coso , then prove that tane = 1 or|-

If cosA+cos^(2)A=1 , then prove that sin^(2)A+sin^(4)A=1 .

If cosA+cos^(2)A=1 , then prove that sin^(2)A+sin^(4)A=1 .

If sin^4 A + sin^2 A=1 then prove that 1/(tan^4A)+1/(tan^2A)=1

If (cos^(4)alpha)/(cos^(2) beta) + (sin^(4)alpha)/(sin^(2)beta) = 1, prove that sin^(4)alpha + sin^(4) beta = 2 sin^(2) alpha sin^(2) beta

f1+sin^(^^)@0=3sin e cose , then prove that tane =1 or

if sin^4x+sin^2x=1 ,then prove that cot^4x+cot^2x =1.

If (cos^4 alpha)/(cos^2 beta)+ (sin^4 alpha)/(sin^2 beta) =1 , prove that : sin^4 alpha+ sin^4 beta= 2 sin^2 alpha sin^2 beta .