Show that the following two equations represent the same set of angles.
`x + pi/4 = npi + (-1)^(n). pi/6` and `x-pi/4 = 2npi +- pi/3`

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

Which of the following is not the general solution of 2^(cos2x)+1=3. 2^(-sin^2 x)? (a) npi,n in Z (b) (n+1/2)pi,n in Z (c) (n-1/2)pi,n in Z (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

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

The value of 3 sin (pi/6) "sec" (pi/3) - 4 sin (5pi/6) cot (pi/4) is-

If cosx + sinx = cos alpha- sinalpha , prove that, x-pi/4 = 2npi +-(alpha + pi/4)

The angle between the tangents to the curve y=x^2-5x+6 at the point (2, 0) and (3, 0) is (a) pi/2 (b) pi/3 (c) pi (d) pi/4

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

If (cos e c^2theta-4)x^2+(cottheta+sqrt(3))x+cos^2(3pi)/2=0 holds true for all real x , then the most general values of theta can be given by n in Z) 2npi+(11pi)/6 (b) 2npi+(5pi)/6 2npi+-(7pi)/6 (d) npi+-(11pi)/6

The sum of all the solution in [0,4pi] of the equation tanx+cotx+1=cos(x+pi/4)i s (a) 3pi (b) pi/2 (c) (7pi)/2 (d) 4pi