If cos (A + B) sin (C + D)= cos (A - B) sin (C- D), prove that tanAtanBtanC = tanD

If A + B + C= pi and cos A = cos B cos C, show that tan A =tan B + tan C and cot B cot C=1/2.

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 cos ((A+B)/2) = sin (c/2) .

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

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

If sin (B + C-A)= 1, cos(C+ A- B)=1,.tan (A+ B - C)= 1 and if A,B,Care positive and acute angles, find A,B,C.

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

If x=sin t, y=cos t , then find (d y)/(dx) .

If A + B + C= pi , prove that sin 2A + sin 2B -sin 2C =4cos A cos B sin C