For a positive integer `n ,` let `f_n(theta)=(tantheta//2)(1+sectheta)(1+sec2theta)(1+sec4theta)...................(1+sec2^ntheta)`. Then (a)`f_2(pi/(16))=1` (b) `f_3(pi/(32))=1` (c)`f_4(pi/(64))=1` (d) `f_5(pi/(128))=1`

Prove that (1+sec 2 theta) (1+sec 4 theta)........(1+sec 2^(n) theta)=tan 2^(n) theta cot theta

Prove that: (tantheta)/(sectheta -1) = (tan theta + sec theta + 1)/(tan theta + sec theta -1)

Prove that: (1+sec2theta)(1+sec4theta)(1+sec8theta)(1+sec2^ntheta)=t a n2^nthetacottheta, n in Ndot

Prove that (1+sec 2 theta)(1+sec 4 theta)(1+sec 8 theta)=(Tan 8theta)/(tan theta)

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

(1-Sin^(2)theta)(sec^(2)theta)= ………… .

If theta=pi/(2^n+1) , prove that: 2^ncosthetacos2thetacos2^2theta....... cos2^(n-1)theta=1.

If theta=pi/(4n) then the value of tanthetatan(2theta)tan(3theta)....tan((2n-1)theta) is

If (sec theta - 1)(sec theta + 1) = 1/3, then cos theta = …………

Let f_n(theta)=(cos(theta/2)+cos2theta+cos((7theta)/2)+....+cos(3n-2)(theta/2))/(sin(theta/2)+sin2theta+sin((7theta)/2)+....+sin(3n-2)(theta/2)) then (a) f_3((3pi)/(16))=sqrt(2)-1 (b) f_5(pi/(28))=sqrt(2)+1 (c) f_7(pi/(60))=(2+sqrt(3)) (d) none of these