Simplify : `sin theta (cosec theta - sin theta)`

[[ Simplify :cos thetacos theta,sin theta-sin theta,cos theta]]+sin theta[[sin theta,-cos thetacos theta,sin theta]]

Simplify [(sin theta)/(cos theta)+(cos theta)/(sin theta)]^(2)

Simplify, costheta[[cos theta, sin theta],[-sin theta, cos theta]] + sin theta [[sin theta, -cos theta],[cos theta, sin theta]]

Prove the following identity : sin theta cot theta+ sin theta cosec theta=1 + cos theta .

Simplify: (sin^(3) theta + cos^(3) theta)/(sin theta + cos theta) + sin theta cos theta

If ("cosec" theta+sin theta)/("cosec" theta-sin theta)=(5)/(3) , calculate the value of sin theta .

(cosec theta+sin theta)(cosec theta-sin theta)=cot^(2)theta+cos^(2)theta

Prove the following identity : (sin theta)/(cot theta+ cosec theta)=2+ (sin theta)/(cot theta- cosec theta) .

Eliminate theta from the equation s=sin theta +"cosec" theta and r= sin theta-"cosec" theta .