If ` cos ^2 ( pi /6 + x ) - sin ^ 2 ( pi/ 6 - x ) = K cos 2 x` , then K is .
(a) 1
(b) -1
(c) 1/2
(d) 2

If f(x)={(sin(cosx)-cosx)/((pi-2x)^2)\ \ \ ,\ \ \ x!=pi/2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \k\ \ \ \ ,\x=pi/2 is continuous at x=pi/2 , then k is equal to (a) 0 (b) 1/2 (c) 1 (d) -1

Solve : cos ^(-1) x + sin ^(-1) "" (x)/( 2) = (pi)/(6)

If cos 3x+sin (2x-(7pi)/6)=-2 , then x is equal to (k in Z)

If sin^(-1)x-cos^(-1)x=pi/6 , then x= (a) 1/2 (b) (sqrt(3))/2 (c) -1/2 (d) none of these

The value of cos^2(pi/6+theta)-sin^2\ \ (pi/6-theta) is a, 1/2cos2theta b. 0 c. -1/2cos2theta d. -cot35^0

If 2 sin^(2) ((pi//2) cos^(2) x)=1-cos (pi sin 2x), x ne (2n + 1) pi//2, n in I , then cos 2x is equal to

If sin^(-1)(x-1)+cos^(-1)(x-3)+tan^(-1)(x/(2-x^2))=cos^(-1)k+pi, then the value of k is (a)1 (b) -1/(sqrt(2)) (c) 1/(sqrt(2)) (d) non of these

The equation 2 sin^(2) (pi/2 cos^(2) x)=1-cos (pi sin 2x) is safisfied by

If |sin^(-1)x|+|cos^(-1)x|=pi/2,t hen (a) x inR (b) [-1,1] (c) [0,1] (d) varphi

Suppose 3 sin ^(-1) ( log _(2) x ) + cos^(-1) ( log _(2) y) =pi //2 " and " sin^(-1) ( log _(2) x ) + 2 cos^(-1) ( log_(2) y) = 11 pi//6 , then the value of x^(-2) + y^(-2) equals