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

Prove that (1+sin2theta)/(1-sin2theta)=((1+tantheta)/(1-tan theta))^(2)

Prove that, (2costheta+1)(2costheta-1) (2cos2theta-1)(2cos4theta-1)=2cos8theta+1

Prove that (sin theta -cos theta+1 )/( sin theta + cos theta -1) =(1)/( sec theta -tan theta ) [use the identity sec ^(2) theta =1 +tan ^(2) theta ]

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

If theta_(1), theta_(2), theta_(3), theta_(4),….., theta_(n) are in AP whose common difference is d, show that sec theta_(1) sec theta_(2) + sec theta_(2) sec theta_(3)+ ………+ sec theta_((n-1)) sec theta_(n)= (tan theta_(n)- tan theta_(1))/(sin d)

Let theta in (0,pi/4) and t_1=(tan theta)^(tan theta), t_2=(tan theta)^(cot theta), t_3=(cot theta)^(tan theta) and t_4=(cot theta)^(cot theta), then

By using above basic addition/ subtraction formulae, prove that (i) tan (A+B)=(tan A+tan B)/(1-tan A tan B) , (ii) tan (A-B)=(tan A-tanB)/(1+tan A tan B) (iii) sin2theta=2sintheta costheta , (iv) cos2theta=cos^(2)theta=1-2sin^(2)theta=2cos^(2)theta-1 (v) tan 2theta=(2 tan theta)/(1-tan^(2) theta)

(i) The points (-1, 0), (4, -2) and (cos 2theta, sin 2 theta) are collinear (ii) The points (-1,0), (4, -2) and ((1-tan^(2)theta)/(1+tan^(2)theta),(2tan theta)/(1+tan^(2)theta)) are collinear

Prove the following identities : (1+tan^(2)theta)/(1+cot^(2)theta)=((1-tantheta)/(1-cottheta))^(2)

Prove that (cot theta -cos theta )/( cot theta +cos theta ) =(cos ec theta -1)/( cosec theta +1)