Simplify `cot(theta - (13pi)/2)`

Convert the following into simplest form (v) cot (theta- (13 pi)/(2))

Simplify: cos^(2)theta+(1)/(1+cot^(2)theta):

Simplify (1-cos theta ) (1+cos theta ) (1+ cot ^(2) theta) .

Simplify (1-cos theta ) (1+cos theta ) (1+ cot ^(2) theta) .

If 3cot(theta-(pi)/(12))=cot(theta+(pi)/(12))

Prove that (sin(3pi-theta)cos(theta- pi/2)tan((3pi)/(2)-theta))/(cosec((13pi)/(2)+theta)sec(3pi+theta)cot(theta- pi/2))=cos^(4)theta

If (-pi)/(2) lt theta lt (pi)/(2) and theta ne +- (pi)/(4) , then the value of cot((pi)/(4) + theta)cot((pi)/(4)-theta) is