If ` cos^2 A - sin^2 A = tan^2 B` then prove that ` 2 cos^2 B -1 = tan^2 A`

If tan A=1//2, tan B=1//3 , then prove that cos 2A=sin2B .

If cos^2alpha-sin^2alpha=tan^2beta," then prove that "tan^2alpha=cos^2beta-sin^2beta .

If tan x = b/a, prove that a cos 2x + b sin 2x=a

If tan A = n tan B and sin A = m sin B, prove that : cos^(2) A = (m^(2) - 1)/(n^(2) - 1)

Prove that: (cos2A)/(1+sin2A) = tan(pi/4-A)

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

If tan^2 theta = 1+2 tan^2 phi , prove that cos 2 phi = 1 + 2 cos 2 theta .

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

If (cos^4A)/(cos^2B)+(sin^4A)/(sin^2B)=1 , then prove that (i) sin^4A+sin^4B=2 sin^2Asin^2B (ii) (cos^4B)/(cos^2A)+(sin^4B)/(sin^2A)=1

Prove: ( sin 2 A)/( 1 + cos 2 A)= tan A