If `theta_(1),theta_(2),theta_(3),".......",theta_(n)` are in AP whose common difference is d, then show that `sind{sectheta_(1) sectheta_(2) sectheta_(2)sectheta_(3)+"........"+sectheta_(n-1)sectheta_(n)}=tantheta_(n)-tantheta_(1)`.

If theta_(1),theta_(2),theta_(2), theta_(3),"…………" Theta_(n) are in AP whose common difference is d, show that sec theta_(1) sec theta_(2)+ sec_(3) +" …" + sec theta _(n-1)sec theta_(n)=(tantheta_(n)-tan theta_(1))/(sin d )

Prove that (1+sintheta)/costheta+costheta/(1+sintheta)=2sectheta .

For theta_(1), theta_(2), ...., theta_(n) in (0, pi/2) , if ln(sec theta_(1)-tan theta_(1))+ "ln" (sec theta_(2)-tan theta_(2))+...... +"ln" (sec theta_(n)-tan theta_(n))+"ln" pi=0 , then the value of cos((sec theta_(1)+ tan theta_(1))(sec theta_(2)+tan theta_(2))....(sec theta_(n)+tan theta_(n))) is equal to

If tan m theta = tan n theta and general value of theta are in AP, then common difference is

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

Prove tantheta/(sectheta-1)+(tantheta)/(sectheta+1)=2cosectheta .

Prove that (sectheta+tantheta)(1-sintheta)=costheta .

Prove that (1-sintheta)/(1+sintheta)=(sectheta-tantheta)^2 .

If cottheta=3/4 prove that sqrt((sectheta-cosectheta)/(sectheta+cosectheta))=1/sqrt7 .