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

Prove that (sin A+sin B)/(cos A+cos B)=tan((A+B)/2)

If A +B = 90 , prove that (sin A- sin B)^2 = 1-2 sin A cos A .

Prove any one of the following: (sin 5A-2sin 3A+sin A)/(cos 5A-cos A)=tan A

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

Prove that (sin^3A+cos^3A)/(sin A+cos A)+(sin^3A-cos^3A)/(sin A-cos A)=2

Prove that: ((sin 0+sin 60)(cos 60+tan 45)/(tan 30+cot 60)(cosec 30-cosec 90))=(9/8)

Prove that: (2 sin 68°)/(cos 22°)-( 2 cot 15°)/( 5 tan 75°)- 3( tan 45° tan 20° tan 40 tan 50° tan 70°)/5 = 1 .

Show that (cos A)/(1-tan A)+(sin A)/(1-cot A)=sin A +cos A

If A +B = 90 , prove that (tan A + cosec B)^2=(1+sin A)/(1- cos B) .

If A +B = 90 , prove that (cos A + cos B)/(sin A+ sinB)=1 .