If `f(theta)=|cos^2thetacosthetasintheta-sinthetacosthetasinthetasin^2thetacosthetasintheta-costheta0|,t h e r ef(pi/3)+f((2pi)/3)+f(pi)+f((4pi)/3)++f((npi)/3)` is equal to `n` (b) `(n(n+1))/2` (c) `n^2+2n` (d) `2n^2-n`

If f(theta)=lim_(n rarr oo)cos theta cos2 theta cos2^(2)theta...*cos2^(n-1)theta, then |(1)/(pi)f((3 pi)/(2))|

If sin^(3)theta+sin theta cos^(2)theta=1, then theta is equal to (n in Z)( a) 2n pi(b)2n pi+(pi)/(2)(c)2n pi-(pi)/(2) (d) n pi

A general solution of tan^(2)theta+cos2 theta=1 is (n in Z)n pi=(pi)/(4) (b) 2n pi+(pi)/(4)n pi+(pi)/(4) (d) n pi

f(n,theta)=(1+sec2 theta)(1+sec2^(2)theta)...(1+sec2^(n)theta) then f(1,(pi)/(6)) and f(2,(pi)/(12))=

The sum of all the solutions of cot theta=sin2 theta(theta!=n pi,n integer) 0<=theta<=pi, is (a) (3 pi)/(2) (b) pi (c) 3(pi)/(4) (d) 2 pi

If cot theta-tan theta=sec theta, then theta is equal to 2n pi+(3 pi)/(2),nZ b.n pi+(-1)^(n)(pi)/(6),nZ c.n pi+(pi)/(2),nZ d.none of these

The value(s) of theta , which satisfy 3-2\ costheta-4sintheta-cos2theta+sin2theta=0 is/are theta=2npi; n in I (b) 2npi+pi/2; n in I 2npi-pi/2; n in I (d) npi: n in I

The expression cos3 theta+sin3 theta+(2sin2 theta-3)(sin theta-cos theta) is positive for all theta in (2n pi-(3 pi)/(4),2n pi+(pi)/(4)),n in Z(2n pi-(pi)/(4),2n pi+(pi)/(6)),n in Z(2n pi-(pi)/(3),2n pi+(3 pi)/(3)),n in Z(2n pi-(pi)/(4),2n pi+(3 pi)/(4)),n in Z

If A=[cos theta-sin theta sin theta cos theta], then A^(T)+A=I_(2), if theta=n pi,n in Z(b)theta=(2n+1)(pi)/(2),quad n in Z(c)theta=2n pi+(pi)/(3),quad n in Z(d) none of these

If (1)/(6)sin theta,cos theta and tan theta are in GP,then the general value of theta is (i) 2n pi+-(pi)/(3)( ii) 2n pi+-(pi)/(6) (iii) 2n pi+-(-1)^(n)(pi)/(3)( iv )n pi+-(pi)/(3)