Question

# ( frac{sin left(90^{circ}-thetaright) sec left(180^{circ}-thetaright) sin (-theta)}{sin left(180^{circ}+thetaright) cot left(360^{circ}-thetaright) operatorname{cosec}left(90^{circ}+thetaright)} )

Solution

( frac{sin (90-theta) sec (180-theta) sin (-theta)}{sin (180+theta) cot left(360^{circ}-thetaright) operatorname{cosec}(90+theta)} )

( =frac{(cos theta)(+sec theta) cdot(+sin theta)}{(+sin theta)(+cot theta)(sec theta)} )

( =frac{cos theta}{cot theta} )

( =frac{cos theta}{sin theta} )

( =frac{cos theta sin theta}{sin theta} )

( =sin theta )