Consider the system linear equations in `x ,y ,a n dz` given by `(sin3theta)x-y+z=0,(cos2theta)x+4y+3z=0,2x+7y+7z=0.` the value of `theta` for which the system has a non-trivial solution :
(A) `theta = npi/2`
(B) `theta = (2n+1)pi/6`
(C) `theta = npi or npi + (-1)^n pi/6`
(D) none of these

Consider the system of linear equations in x , ya n dz : ""(sin3theta)x-y+z=0 , (cos2theta)x+4y+3z=0 , 2x+7y+7z=0 Which of the following can be the value of theta for which the system has a non-trivial solution (A) npi+(-1)^npi/6,AAn in Z (B) npi+(-1)^npi/3,AAn in Z (C) npi+(-1)^npi/9,AAn in Z (D)none of these

Consider the system of equations : x sintheta-2ycostheta-az=0 , x+2y+z=0 , -x+y+z=0 , theta in R

Find the value theta for which the homogeneous system of equations: (sin 3 theta) x-y+z=0 , (cos2theta) x+4y+3z=0 and 2x+7y+7z=0 has non-trivial solutions.

The value of k for which the system of equations x+ky-3z=0 , 3x+ky-2z=0, 2x+3y-4z=0 has a non -trivial solution is

A general solution of tan^2theta+cos2theta=1 is (n in Z) npi=pi/4 (b) 2npi+pi/4 npi+pi/4 (d) npi

Show that the following two equations represent the same set of angles: theta - pi/6 = 2npi +-pi/3 and theta + pi/3 = npi + (-1)^(n) pi/6

The value of theta ( 0 lt theta lt (pi)/(2)) for which cos theta sin (theta - (pi)/(6)) is maximum is-

If (sin theta) (x) = (cos theta)/(y) , then prove that sin theta - cos theta = (x - y)/(sqrtx^2 + y^2) .

The straight line xcostheta+ysintheta=2 will touch the circle x^2+y^2-2x=0 if (a) theta=npi,n in I Q (b) A=(2n+1)pi,n in I (c) theta=2npi,n in I (d) none of these

Which of the following is not the solution of the equation sin5x=16sin^5x(n in Z)? (a) npi (b) npi+pi/6 (c) npi-pi/6 (d) none of these