The expression `cos3theta+sin3theta+(2sin2theta-3)(sintheta-costheta)` is positive for all `theta` in (a) `(2npi-(3pi)/4,2npi+pi/4),n in Z` (b) `(2npi-pi/4,2npi+pi/6),n in Z` (c)`(2npi-pi/3,2npi+pi/3),n in Z` (d)`(2npi-pi/4,2npi+(3pi)/4),n in Z`

If sin^3theta+sinthetacos^2theta=1,t h e ntheta is equal to (n in Z) (a) 2npi (b) 2npi+pi/2 (c) 2npi-pi/2 (d) npi

Let tanx-tan^2x >0 and |2s inx| npi,n in Z (b) x > npi-pi/6,n in Z x

If (costheta+cos2theta)^3=cos^3theta+cos^3 2theta, then the least positive value of theta is equal to pi/6 (b) pi/4 (c) pi/3 (d) pi/2

If sintheta=1/2a n dcostheta=-(sqrt(3))/2, then the general value of theta is (n in Z)dot (a) 2npi+(5pi)/6 (b) 2npi+pi/6 2npi+(7pi)/6 (d) 2npi+pi/4

Solution of the equation sin(sqrt(1+sin2theta))=sintheta+costhetai s(n in Z) (a) npi-pi/4 (b) npi+pi/(12) (c) npi+pi/6 (d) none of these

The general solution of the equation sin^(100)x-cos^(100)x=1 is 2npi+pi/3,n in I (b) n pi+pi/2,n in I npi+pi/4,n in I (d) 2npi=pi/3,n in I

If the line xcostheta+ysintheta=P is the normal to the curve (x+a)y=1, then show theta in (2npi+pi/2,(2n+1)pi)uu(2npi+(3pi)/2,(2n+2)pi),n in Z

One of the general solutions of 4sinthetasin2thetasin4theta=sin3theta is (3n+-1)pi/(12),AAn in Z (3n+-1)pi/9,AAn in Z (3n+-1)pi/(12),AAn in Z (3n+-1)pi/3,AAn in Z

If |2 sin theta-cosec theta| ge 1 and theta ne (n pi)/2, n in Z , then

If the vectors vec aa n d vec b are linearly idependent satisfying (sqrt(3)tantheta+1 )veca+(sqrt(3)s e ctheta-2) vec b=0, then the most general values of theta are a. npi-pi/6, n in Z b. 2npi+-(11pi)/6, n in Z c. npi+-pi/6, n in Z d. 2npi+(11pi)/6, n in Z