If `a+b=pi/2`and `sin a=1/x`,then the value of `cos2b` will be (Consider `180^(@)`to be `pi`)

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

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)

If tan^(-1)(x^(2)+3|x|-4)+cot^(-1)(4 pi+sin^(-1)sin14)=(pi)/(2), then the value of sin^(-1)sin2x is (a)6-2 pi( b) 2 pi-6( c) pi-3 (d) 3-pi

If sinA=3/5 and cosB=9/41, 0 < A < pi/2 and 0 < B < pi/2 then find the values of (i) sin(A+B) (ii) sin(A-B) (iii) cos(A+B) (iv) cos(A-B)

f(x)={x+sqrt(2)a sin x,0

If (cos A)/3= (cos B)/4= 1/5, - pi/2 lt A lt 0 and - pi/2 lt B lt 0 then the value of 2 sin A + 4 sin B is

Let us consider the equation cos^4x/a+sin^4x/b=1/(a+b),x in[0,pi/2],a,bgt0 The value of sin^2x in terms of a and b is

If f(x)={(((1-sin^(3)x))/(3cos^(2)x)",",x lt (pi)/(2)),(a",",x=(pi)/(2)),((b(1-sinx))/((pi-2x)^(2))",",x gt (pi)/(2)):} is continuous at x=(pi)/(2) , then the value of ((b)/(a))^(5//3) is

If sin A = (1)/(2) , cos B = 1, 0 lt A, B le (pi)/(2) then find the value of (A + B).