If `A=[{:(cos x,-sin x),(sin x,cos x):}]` ,then `A+A^(-1)=I` if the value of `x` is
a.`(pi)/(6)`
b.`(pi)/(3) `
c. `""` ` pi`
d.`(3 pi)/(2)`

Maximum value of sin (x + (pi)/(6)) + cos (x + (pi)/(6)) is

If cos^(-1) x = (pi)/(3) , the find the value of sin ^(-1)x .

If sin^(-1)x+sin^(-1)y=(2 pi)/(3) ,then the value of cos^(-1)x+cos^(-1)y is (A) (2 pi)/(3) (B) (pi)/(3) (C) (pi)/(2) (D) pi

f(x)=|2cos^(2)x sin2x-sin x sin2x2sin^(2)x cos x sin x-cos x0| Then the value of int_(0)^( pi/2)[f(x)+f'(x)]dx is a. pi b.pi/2c.2 pi d.3 pi/2

" sin " (x-(pi)/(6)) + " cos " (x-(pi)/(3)) =sqrt(3) " sin " x

Prove that (i) cos (n + 2) x cos (n+1) x +sin (n+2) x sin (n+1) x = cos x) (ii) " cos " .((pi)/(4)-x) " cos " .((pi)/(4)-y) " - sin " ((pi)/(4)-x ) " sin " ((pi)/(4) -y) =" sin " (x+y)

If 4cos x sin x*2sin x = 3sin x, then x = (i) n pi+(-1)^(n) (pi)/(10) (ii) n pi-(-1)^(n) ( pi)/(10) (iii) 2n pi+-(pi)/(10) (iv) n pi+(pi)/(10)

Let 2y={(cot^(-1)(sqrt(3)cos x-sin x))/(cos x+sqrt(3)sin x))^(2) then (dy)/(dx) is equal to (A) x-(pi)/(6)(B)x+(pi)/(6)(C)2x-(pi)/(6)(D)2x-(pi)/(3)])

lim_ (x rarr (pi) / (6)) (2 (sin x cos ((pi) / (6)) - cos x sin ((pi) / (6)))) / (x- (pi) / (6))

If sin^(-1)x+sin^(-1)y=(pi)/(3) and cos^(-1)x+cos^(-1)y=(pi)/(6), find the values of x and y.