If `cos A+sin B=m` and `Sin A+cos B=n`,then prove that `2sin (A+B)=m^2+n^2-2`.

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

In a ∆ ABC prove that sin( (A+B)/2) = COS (c/2) .

In a ∆ ABC prove that cos ((A+B)/2) = sin (c/2) .

If a cos theta +bsin theta=x and a sin theta-b cos theta = y then prove that a^2+b^2=x^2+y^2

If sin A=sin B and cos A = cosB, find A in terms of B

If A and G be the A.M. and G.M. of two numbers a and b and A:G=m:n ,then prove that- a:b=m+sqrt(m^2-n^2) :m-sqrt(m^2-n^2)

If cos theta+sin theta=sqrt 2 cos theta ,then prove that cos theta-sin theta = sqrt 2 sin theta .

If cos^2theta- sin^2theta= tan^2 phi , then prove that cos^2phi – sin^2phi= tan^2theta

If a costheta -b sin theta = c ,then prove that a sintheta + b costheta=+-sqrt(a^2+b^2-c^2 )

If P(x) =[(cos x, -sin x),(sin x , cos x)] , then show that P(A) P(B)=P(A+B) .