" 6."tan theta sin(pi/2+theta)cos(pi/2-theta)=

If tan theta = 3/4 and theta is not in the first quadrant then (sin (pi//2 + theta)-cot(pi-theta))/(tan(3 pi//2 - theta)-cos (3pi//2+theta))=

cos^2(pi/6+theta)-sin^2(pi/6-theta)=

Prove that : (cos(pi+theta)cos(-theta))/(sin (pi-theta) cos (pi/2+ theta))= cot^2 theta.

If tan theta=(3)/(4) and theta is not in first quadrant sin(sin((pi)/(2)+theta)-cot(pi-theta))/(tan((3 pi)/(2)-theta)-cos((3 pi)/(2)+theta))=

Show that : (1+ tan theta/2)/(1-tan theta/2) = (1+sin theta)/(cos theta) = tan (pi/4 + theta/2)

If "cosec"(pi//2+ theta )+x cos theta cot(pi//2-theta )=sin(pi//2+ theta ), then x =

Prove that: (cos(2 pi+theta)csc(2 pi+theta)tan(pi/2+theta))/(sec(pi/2+theta)cos theta cot(pi+theta))=1

Prove that (cos (pi-theta).cot(pi/2 +theta).cos(-theta))/(tan(pi+theta).tan((3pi)/(2)+theta).sin(2pi-theta))=cos theta

Prove that : sqrt((1-sin theta)/(1+sin theta))= {(sec theta- tan theta, if -pi/2 < theta< pi/2), (-sec theta+ tan theta, if pi/2 < theta< (3 pi)/2):} .

If f(theta)=|(cos^(2)theta ,cos theta sin theta, -sin theta),(cos theta sin theta, sin^(2)theta,cos theta),(sin theta,-cos theta,0)| then, f((pi)/(6))+f((pi)/(3))+f((pi)/(2))+f((2pi)/(3))+f((5pi)/(6))+f(pi)+……+f((53pi)/(6)) is equal to