" 18."(1)/(1+sin x)

" (1) "int(1+sin x)/(1-sin x)dx

(cos x)/(1-sin x)=(1+cos x+sin x)/(1+cos x-sin x)

sqrt((1+sin x)/(1-sin x))

The value of lim_(xrarr0) {1^((1)/(sin^(2)x)+)2^((1)/(sin^(2)x))+3^((1)/(sin^(2)x))+.....+n^((1)/sin^(2)x)}^(sin^2x) , is

Tan ^(-1) (sqrt ((1 - sin x )/( 1 + sin x )))

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))