If `2^(sqrt(sin^(2)x-2sin x+5)-2sin^(3)y)<=1` then number of ordered pairs (x,y) in `[0,2 pi]`

if (2sqrt(sin^(2)x-2sin x+5))/(4^( sin ^(2)y))<=1 then which option is correct.

All the pairs (x,y) that satisfy the inequality 2^(sqrt(sin^(2)x-2sin x+5))*(1)/(4^(sin^(2)y))<=1 also satisfy the equation :

sqrt(3|sin x|-sin x-2)

Evaluate: int(cos x)/(sqrt(sin^(2)x-2sin x-3))dx

Evaluate: int(cos x)/(sqrt(sin^(2)x-2sin x-3))dx

The value of lim_(x rarr(pi)/(2))tan^(2)x(sqrt(2sin^(2)x+3sin x+4)-sqrt(sin^(x)+6sin x+2)) is equal to

Evaluate the value of lim_(n rarr(pi)/(2))tan^(2)x sqrt((2sin^(2)x+3sin x+4)-sqrt(sin^(2)x+sin x+2))

Find the value of x in [-pi,pi] for which f(x)=sqrt(log_(2)(4sin^(2)x-2sqrt(3)sin x-2sin x+sqrt(3)+1)) is defined.

lim_(x to 0) (x +2 sin x)/(sqrt(x^(2)+2 sin x + 1)-sqrt(sin^(2) x - x+ 1)) is

sin^(-1)[sqrt(x^(2)-x^(3))-sqrt(x-x^(3))]=..... a) sin^(-1)x+sin^(-1)sqrt(x) b) sin^(-1)x-sin^(-1)sqrt(x) c) sin^(-1)sqrt(x)-sin^(-1)x d) 2sin^(-1)x