Let `tanx-tan^2x >0` and `|2s inx|<1` . Then the intersection of which of the following two sets satisfies both the inequalities? `x > npi,n in Z` (b) `x > npi-pi/6,n in Z` `x

Which of the following is not the general solution of 2^(cos2x)+1=3. 2^-sin^(2x)? (a)npi,n in Z (b) (n+1/2)pi,n in Z (n-1/2)pi,n in Z (d) none of these

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

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

Consider the system of linear equations in x , ya n dz : ""(sin3theta)x-y+z=0(cos2theta)x+4y+3z=0 3x+7y+7z=0 Which of the following can be the value of theta for which the system has a non-trivial solution npi+(-1)^npi/6,AAn in Z npi+(-1)^npi/3,AAn in Z npi+(-1)^npi/9,AAn in Z none of these

If sinx+cosy=1 and cos2x-cos2y=1 then the values of x and y are (A) x=npi+(-1)^n pi/3, n in I, y=mpi+-pi/6, m in I (B) x=npi+(-1)^n pi/6, n in I, y=mpi+-pi/3, m in I (C) x=npi+(-1)^n pi/4, n in I, y=mpi+-pi/4, m in I (D) none of these

The product of matrices A=[[cos^2theta,costheta],[sinthetacostheta,sinthetasin^2theta]] and B=[[cos^2phicosphi,sinphicosphi],[sinphi,sin^2phi]] is a null matrix if theta-phi= (A) 2npi,n in Z (B) (npi)/2, n in Z (C) (2n+1)pi/2, n in Z (D) npi, n in Z

The value(s) of theta, which satisfy the equation : 2cos^3 3thetatheta+4=3sin^2 3theta is/are (2npi)/3+(2pi)/9,\ n in I (b) (2npi)/3-(2pi)/9,\ n in I\ (2npi)/5+(2pi)/5,\ n in I\ (d) (2npi)/5-(2pi)/5,\ n in I

The general solution of the equation sin^(110)x-cos^(100)x=1 is 2n pi+(pi)/(3),n in I(b)npi+(pi)/(2),n in In pi+(pi)/(4),n in I(d)2n pi=(pi)/(3),n in I

General solution of sin^(2)x-5sin x cos x-6cos^(2)x=0 is x=n pi-(pi)/(4),n in Z only npi+tan^(-1)6,n in Zonly both (a) and (b) none of these

If x+y=pi/4a n dtanx+tany=1,t h e n(n in Z) (a)sinx=0a l w a y s (b)when x=npi+pi/4t h e ny=-npi (c)when x=npit h e ny=npi+(pi/4) (d)when x=npi+pi/4t h e ny=npi-(pi/4)