Prove that : `(tan A + tan B)/(tan A - tan B) = (sin (A+B))/(sin(A-B))`

Prove that : (cot A + tan B)/ (cot B + tan A) = cot A tan B

By using above basic addition/ subtraction formulae, prove that (i) tan (A+B)=(tan A+tan B)/(1-tan A tan B) , (ii) tan (A-B)=(tan A-tanB)/(1+tan A tan B) (iii) sin2theta=2sintheta costheta , (iv) cos2theta=cos^(2)theta=1-2sin^(2)theta=2cos^(2)theta-1 (v) tan 2theta=(2 tan theta)/(1-tan^(2) theta)

In any Delta ABC , prove that : ((a-b)/c) = (tan (A/2) - tan (B/2))/(tan (A/2) + tan (B/2)

Prove that : (1 + cot A + tan A) (sin A — cos A) = sin A tan A — cot A cos A.

Prove that : (1 + cot A + tan A) (sin A — cos A) = sin A tan A — cot A cos A.

Prove that: (sin A+sin B)/(sin A-sin B)=tan((A+B)/2)cot((A-B)/2)

If A+B+C=pi , prove that : tan( A/2) tan (B/2) + tan (B/2 )tan (C/2)+ tan( C/2) tan (A/2) =1

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

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

Prove that :(tan(A+B))/("cot"(A-B))=(sin^2A-sin^2B)/(cos^2A-sin^2B)