Prove that `(cos(90^0+theta)sec(-theta)"tan"(180^0-theta))/(sec(360^0-theta)sin(180^0+theta)cot(90^0-theta))=-1`

Prove that: (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

Without using Trigonometric Tables evaluate the following :- sinthetacostheta-(sinthetacos(90^@-theta) costheta)/(sec(90^@-theta))-(costhetasin(90^@-theta)sintheta)/(cosec(90^@-theta)) .

Prove that : (cosec theta)/(cosec theta-1)+ (cosec theta)/ (cosec theta+1)= 2 sec^2 theta .

Prove that sec^4theta-sec^2theta=tan^4theta+tan^2theta .

Prove that cos theta+ sin (270^@-theta)- sin (270^@-theta)+ cos (180^@+theta)=0 .

Simplify the following : (sin (- theta) tan(180^@ +theta) tan (90^@ +theta))/(cot (90^@-theta)cos (360^@-theta) sin (180^@-theta)) .

If (cos theta_(1))/(cos theta_(2))+(sin theta_(1))/(sin theta_(2))=(cos theta_(0))/(cos theta_(2))+(sin theta_(0))/(sin theta_(2))=1 , where theta_(1) and theta_(0) do not differ by can even multiple of pi , prove that (cos theta_(1)*cos theta_(0))/(cos^( 2)theta_(2))+(sin theta_(1)*sin theta_(0))/(sin^(2) theta_(2))=-1

Simplify the following : (cos (360^@-theta) cosec (180^@+ theta) cot (90^@-theta))/(sec (90^@+theta)cos (-theta)) .

Prove that (1 +cot theta -cosec theta )(1+tan theta +sec theta )=2.

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