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

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

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

Prove that ( sin 2 A )/( 1 - cos 2 A) = cot A

( sin 4 A sin 3A - sin 5A sin 2A+ sin 7A sin 4A )/(cos 2A cos 3A - cos 2A * cos 7A + cos A * cos 10A )=

If A = 30^(@) , show that : (i) (1 + sin 2A + cos 2A)/(sin A + cos A) = 2 cos A (ii) (cos^(3)A - cos 3A)/(cos A) + (sin^(3)A + sin 3A)/(sin A) = 3

If A= 45^(@) , verify that: (i) sin 2A=2 sin A cos A (ii) cos 2A= cos^(2)A-"sin"^(2)A .

Prove that: (sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = (2)/(sin^(2)A-cos^(2)A)=(2)/(2sin^(2)A-1)=(2)/(1-2 cos^(2)A) .

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."):}.

( cos A - sin A + 1 ) / ( cos A + sin A - 1 ) = cosec A + cot A cosec A + cot A , = using the identity cosec ^ 2 A = 1 + cot^ 2 A .

Prove the following identities : (sin A + cos A)/ (sin A - cos A) + (sin A - cos A)/ (sin A + cos A) = (2)/ (2 sin^(2) A - 1)