`5sin x+4cos x=3rArr4sin x-5cos x=`
a) 4 b) `4sqrt(2)` c) `3sqrt(2)` d)`sqrt(2)`

The area enclosed by the curve y=sin x+cos x and y=|cos x-sin x| over the interval [0,(pi)/(2)] is 4(sqrt(2)-2) (b) 2sqrt(2)(sqrt(2)-1)2(sqrt(2)+1)(d)2sqrt(2)(sqrt(2)+1)

If 4sin^(2)x+(1)/(4)cos ec^(2)x=2,x in(0,(pi)/(2)) then cos^(2)x+5sin x cos x=7sin^(2)x is equal to (A)(10+5sqrt(3))/(4) (B) 10-5sqrt(3)(C)10+5sqrt(3) (D) none of these

If sin^-1(1/3)+sin^-1 (2/3)= sin^-1 x then x is equal to (A) (4+sqrt(5)/9 (B) (4sqrt(2)+sqrt(5)/9 (C) (sqrt(3)+1)/6 (D) 1

If sin x + cos x = sqrt2 * c os x, "then : cos x - sin x = ...... A) sqrt2* cos x B) sqrt2* sin x C) sqrt2* (cos x +sinx) D)none of these

If I=int(sqrt(cot x)-sqrt(tan x))dx, then I equal sqrt(2)log(sqrt(tan x)-sqrt(cot x))+Csqrt(2)log|sin x|cos x+sqrt(sin2x)|+Csqrt(2)log|sin x-cos x+sqrt(2)sin x cos x|+sqrt(2)log|sin(x+(pi)/(4))+sqrt(2)sin x cos x|+C

If cos (sin^(-1)(2/sqrt(5)) + cos^(-1)x) = 0, then x is equal to A) 1/sqrt(5) B) (-2/sqrt(5)) C) (2/sqrt(5)) D) 1

The value of (lim)_(x->0)(sqrt(2)-sqrt(1+cos x))/(sin^2x) is 1/(2sqrt(2)) b. 1/(8sqrt(2)) c. 1/(4sqrt(2))\ d. -1/(4sqrt(2))

The sum of all the solution(s) of the equation sin^(-1)2x=cos^(-1)x is 0 (2) 2/(sqrt(5)) (3) 1/(sqrt(5)) (4) (-1)/(sqrt(5))

The value of the limit lim_(x to pi/2) (4sqrt2)(sin3x +sinx)/((2 sin 2x sin. (3x)/2 +cos. (5x)/2)-(sqrt(2)+sqrt(2)cos 2x +cos. (3x)/2)) is _______

min[(x_(1)-x_(2))^(2)+(3+sqrt(1-x_(1)^(2))-sqrt(4x_(2)))],AA x_(1),x_(2)in R is (a)4sqrt(5)+1 (b) 3-2sqrt(2)(c)sqrt(5)+1(d)sqrt(5)-1