Prove that `(cos^(2)A-sin^(2)B)+1-cos^(2)C`

Prove that : cos^(4) A - sin^(4) A = 2 cos^(2) A - 1

If DeltaABC , prove that: a) sin^(2)A+sin^(2)B-sin^(2)C=2sinAsinBcosC b) cos^(2)A+cos^(2)B-cos^(2)C=1-2sinAcosBsinC c) cos^(2)A+cos^(2)B+cos^(2)C=1-2cosAcosBcosC

Prove that : sin^(2)Acos^(2)B-cos^(2)Asin^(2)B=sin^(2)A-sin^(2)B

In DeltaABC , prove that: a(cos^(2)C/2-cos^(2)B/2)=(b-c).cos^(2)A/2

Prove that a(b^(2) + c^(2)) cos A + b(c^(2) + a^(2)) cos B + c(a^(2) + b^(2)) cos C = 3abc

If A+B+C=180^0 , prove that : cos^2 (A/2) + cos^2 (B/2) - cos^2 (C/2) = 2cos (A/2) cos (B/2) sin (C/2)

In any DeltaABC , prove that c^(2)=(a-b)^(2)cos^(2)""1/2C+(a+b)^(2)sin^(2)""1/2C

Prove that (1-cos2A+sin2A)/(1+cos2A+sin2A)=tanA

Prove the following identities : tan^(2) A - tan^(2) B = (sin^(2) A - sin^(2) B)/ (cos^(2) A . cos^(2) B)

If A+B+C=180^0 , prove that : cos^2( A/2) + cos^2( B/2) + cos^2(C/2) = 2+2 sin(A/2) sin( B/2) sin( C/2)