" (ix) "f(x)=sqrt(4-x^(2))+(1)/(sqrt(|sin x|-sin x))

If f(x)=sqrt(4-x^(2))+(1)/(sqrt((|sin x|)-sin x)) then the domain of f(x) is

The domain of f(x)=sqrt(1-x^(2))+sqrt(sin(pi sin(pi x))) is

cot^(-1)((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=(x)/(2)

Prove the following: cot^(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))]=(x)/(2),x(0,(pi)/(4))

Prove the following: cot^(-1)((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=(x)/(2),x epsilon(0,(pi)/(4))

Prove the following: cot^(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))]=(x)/(2);x in(0,(pi)/(4))

Prove that: cot^(-1)((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=(x)/(2),x in(0,(pi)/(4))

Prove that: cot^(-1)((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=(x)/(2),x in(0,(pi)/(4))

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.