If `cot theta=7/8`, evaluate:- `((1+sin theta)(1-sin theta))/ ((1+cos theta)(1-cos theta))`

If (cos^(3) theta )/( (1- sin theta ))+( sin^(3) theta )/( (1+ cos theta ))=1+ cos theta , then number of possible values of theta is ( where theta in [0,2pi] )

Find sin 2 theta when sin theta + cos theta= 1 .

If (cos theta_(1))/(cos theta_(2))+(sin theta_(1))/(sin theta_(2))=(cos theta_(0))/(cos theta_(2))+(sin theta_(0))/(sin theta_(2))=1 , where theta_(1) and theta_(0) do not differ by can even multiple of pi , prove that (cos theta_(1)*cos theta_(0))/(cos^( 2)theta_(2))+(sin theta_(1)*sin theta_(0))/(sin^(2) theta_(2))=-1

Prove the following identity : (sin theta)/(1-cos theta)= (1+cos theta)/(sin theta) .

Prove that : (sin theta)/(1+cos theta) + (1+cos theta)/(sin theta)= 2 cosec theta .

If A = [(cos theta, sin theta),(-sin theta, cos theta)] and B = [(sin theta, - cos theta), (cos theta, sin theta)] , evaluate A cos theta + B sin theta .

Prove the following identity : (1-cos theta)/(sin theta)= (sin theta)/(1+cos theta) .

Prove the following identity : cot^2 theta ((sec theta-1)/(1+sin theta))+ sec^2 theta ((sin theta-1)/(1+sec theta)) =0 .

Prove the following identity : 1/(cosec theta- cot theta)-1/(sin theta) =1/(sin theta)- 1/(cosec theta+cot theta) .