The value of `sin(pi/3-sin^(-1)(4/5))` is
(a) `(3sqrt(3)-4)/(10)`
(b) `(3sqrt(3)+4)/(10)`
(c) `(4sqrt(3)-3)/(10)`
(d) `(4sqrt(3)+1)/(10)`

The value of sin(1/4sin^(-1)((sqrt(63))/8)) is (a) 1/(sqrt(2)) (b) 1/(sqrt(3)) (c) 1/(2sqrt(2)) (d) 1/(3sqrt(3))

if cos^(-1)((2)/(3x))+cos^(-1)((3)/(4x))=(pi)/2, x>3/4 then x= (a) (sqrt(145))/(11) (b) (sqrt(145))/(12) (c) (sqrt(146))/(10) (d) (sqrt(146))/(11)

The value of tan{cos^(-1)1/(5sqrt(2))-sin^(-1)4/(sqrt(17))} is (sqrt(29))/3 (b) (29)/3 (c) (sqrt(3))/(29) (d) 3/(29)

The value of tan{cos^(-1)1/(5sqrt(2))-sin^(-1)4/(sqrt(17))} is (sqrt(29))/3 (b) (29)/3 (c) (sqrt(3))/(29) (d) 3/(29)

The value of sin^(-1){cot(sin^(-1)(sqrt((2-sqrt3)/4)+cos^(-1)(sqrt(12)/4)+sec^(-1)sqrt2)} is

Simplify :- (i) (6)/(sqrt(2)) (ii) (sqrt(3))/(3) (iii) sqrt((3)/(4)) (iv) (6)/(sqrt(2)) (v) (sqrt(5))/(10) (vi) sqrt((16)/(2))

The value of x in (0,pi/2) satisfying (sqrt(3)-1)/(sinx)+(sqrt(3)+1)/(cosx)=4sqrt(2) is / are

Given x, y in R , x^(2) + y^(2) gt 0 . Then the range of (x^(2) + y^(2))/(x^(2) + xy + 4y^(2)) is (a) ((10 - 4 sqrt(5))/(3),(10 + 4 sqrt(5))/(3)) (b) ((10 - 4 sqrt(5))/(15),(10 + 4 sqrt(5))/(15)) (c) ((5- 4 sqrt(5))/(15),(5 + 4 sqrt(5))/(15)) (d) ((20- 4 sqrt(5))/(15),(20 + 4 sqrt(5))/(15))

(1)/(sin 10^(@)) - (sqrt3)/(cos 10 ^(@)) = 4.

int_0^(4/pi) (3x^2sin(1/x)-xcos(1/x))dx= (A) (8sqrt(2))/pi^3 (B) (32sqrt(2))/pi^3 (C) (24sqrt(2))/pi^3 (D) sqrt(2048)/pi^3