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

Express sin theta , cos theta , tan theta in terms of cosec theta .

Express sin theta , cos theta , cot theta in terms of sec theta .

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

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

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

If sin A=3/5 , sin B=12/13 and sin C=7/25 where A,B,C are acute angles, find the value of sin (A + B + C).

If A + B + C = 2S, prove that sin (S- A) sin (S - B) +sin S sin (S-C) = sin A sin B

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

Express cos theta , cot theta , tan theta in terms of sin theta .

If A=60⁰ and B=30⁰ , verify that sin (A-B)=sin A cos B-cos A sin B