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

cos((3pi)/2+theta)=

Tan ((pi)/(4)+theta).Tan((3pi)/(4)+theta)=

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

Prove that cos theta + cos[(2pi)/3 + theta] + cos [(4pi)/(3) + theta] = 0 .

If tan theta + tan (pi//3+theta)-tan(pi//3-theta)=3 then theta =

If tan(pi cos theta)=cot(pi sin theta), 0 lt theta lt (3pi)/(4) then sin(theta+(pi)/(4))=

Lt_(theta to pi//2) (1-sin theta)/((pi)/(2))- theta cos theta=

Prove that cos^(2)theta+cos^(2)((2pi)/(3)+theta)+cos^(2)((2pi)/(3)-theta)=(3)/(2)

IF y=(tan(pi/4+theta)+tan(pi/4-theta))/(tan(pi/4+theta)-tan(pi/4-theta)) then find y.

Match the following . {:((1) tan(pi/4+theta)-tan(pi/4-theta)=,(a) 1),((b)tan(pi/4+theta)+cot(pi/4+theta)=,(b)4sec^(2)2theta),((c)tan(pi/4+theta).tan(pi/4-theta)=,(c)2sec2theta),((d)cosec^(2)(pi/4+theta)cosec^(2)(pi/4-theta)=,(d)2tan2theta):}