(4)Find `(sec theta)/(tan theta)`

If 1+ tan^(2) theta = sec^(2) theta then find (sec theta + tan theta)

For theta_(1), theta_(2), ...., theta_(n) in (0, pi/2) , if In (sec theta_(1)-tan theta_(1))+ "In" (sec theta_(2)-tan theta_(2))+...+"In" (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

Locus of the point (sec h theta, tan h theta) is

Prove that : ( sin theta- cos theta +1)/( sin theta +cos theta -1) = (1)/( sec theta - tan theta)

Prove that (tan theta)/(sec theta -1)+ (tan theta)/(sec theta +1) = 2 cosec\ theta

Prove that : (sec 8theta - 1)/(sec 4theta - 1) = (tan 8theta)/(tan 2theta)

prove that : (tan 2^n theta)/(tan theta) = (1+sec 2theta) (1+ sec 2^2 theta) (1+sec 2^3 theta) … (1+ sec 2^n theta)

Prove that : (tan theta)/(1 -cot theta) + (cot theta)/(1- tan theta) = 1 + sec theta cosec theta

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

If a chord joining P(a sec theta, a tan theta), Q(a sec alpha, a tan alpha) on the hyperbola x^(2)-y^(2) =a^(2) is the normal at P, then tan alpha is (a) tan theta (4 sec^(2) theta+1) (b) tan theta (4 sec^(2) theta -1) (c) tan theta (2 sec^(2) theta -1) (d) tan theta (1-2 sec^(2) theta)