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

2cos((pi)/(2)-theta)+3sin((pi)/(2)+theta)-(3sin theta+2cos theta)=

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

Prove that: 4sin theta sin(theta+(pi)/(3))sin(theta+(2 pi)/(3))=sin3 theta

If x sintheta=ysin(theta+(2pi)/(3))=z sin(theta+(4pi)/(3)), then

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

Prove that 4sin theta sin((pi)/(3)+theta)sin((2 pi)/(3)+theta)=sin3 theta

If the vectors vec a and vec b are linearly idependent satisfying (sqrt(3)tan theta+1)vec a+(sqrt(3)sec theta-2)vec b=0 then the most general values of theta are a.n pi-(pi)/(6),n in Z b.2n pi+-(11 pi)/(6),n in Z c.n pi+-(pi)/(6),n in Z d.2n pi+(11 pi)/(6),n in Z

If tantheta+tan2theta+sqrt(3)tanthetatan2theta=sqrt(3) , then theta=(npi)/(3)+(pi)/(9) .

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

If 4cos^(2)theta+sqrt(3)=2(sqrt(3)+1)cos theta, then theta is 2n pi+-(pi)/(3),n in I(b)2n pi+-(pi)/(4),n in I2n pi+-(pi)/(6),n in I(d) none of these