e^(sqrt(sin x))

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(i)e^(cotx)" "(ii)e^(-sin 2x)" "(iii) e^(sqrt(sinx))

f(x)=sqrt(sin(cos x))+ln(-2cos^(2)x+3cos x+1)+e^(cos^(-1))((2sin x+1)/(2sqrt(2sin x)))

int_(0)^(pi//2) (1)/(1+e^(sqrt(2)sin(x-pi//4)))dx=

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

Find the value of cot^(-1)[(sqrt(1-sin x)+sqrt(1+sin x))/(sqrt(1-sin x)-sqrt(1+sin x))]

(cot^(-1){sqrt(1+sin x)+sqrt(1-sin x)})/(sqrt(1+sin x)-sqrt(1-sin x))

the expression ((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=

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

d/(dx) [(e^(sinsqrt(x)) + e^(-sin sqrt(x)))/(e^(sin sqrt(x)) - e^(-sinsqrt(x)))] =