" (ii) "quad (sin A+sin2A)/(cos A-cos2A)=cot(A)/(2)

(sin A-sin B)/(cos B-cos A)=cot((A+B)/(2))

(sin 2x - sin 2y)/(cos 2y-cos 2x) = cot (x+y)

prove that (sin2A)/(1-cos2A)=cot A

prove that ((cos A+cos B)/(sin A-sin B))^(n)+((sin A+sin B)/(cos A-cos B))^(n)=2cot^(n)((A-B)/(2)),n is even

(sin A + sin2A) / (1 + cos A + cos2A) = tan A

Prove that: ((cos A+cos B)/(sin A-sin B))^(n)+((sin A+sin B)/(cos A-cos B))^(n)={2cot^(n)((A-B)/(2)),quad if niseven0,if nisodd

(1-cos2A+sin2A)/(1+cos2A+sin2A)=tanA

(1+sin2A-cos2A)/(1+sin2A+cos2A)=tanA

(1+sin2A-cos2A)/(1+sin2A+cos2A)=tanA

Prove that ((cos A + cos B)/( sin A - sin B )) ^(n) + ((sin A + sin B )/( cos A - cos B )) ^(n) ={{:(2 cot ^(n) ((A- B)/(2)),"," "if n is even."),(0,",""if n is odd."):}.