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

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If =sin x[(1)/(sin x*sin2x)+(1)/(sin2x*sin3x)+...+(1)/(sin nx sin(n+1)x)] then (dy)/(dx)=

if a=(1+sin x)/(1-cos x+sin x) then (1+cos x+sin x)/(2sin x) is

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

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

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))]=

If y = sin x[1/(sin x.sin 2x) + 1/(sin 2x .sin 3x) +...+ 1/(sin nx sin(n + 1)x)] then (dy)/(dx) =

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