`sin x= (2pq)/(p^2+q^2) => cosec x+ cot x=`

sin x=(2pq)/(p^(2)+q^(2))rArr cos ecx+cot x=

sin x=(2pq)/(p^(2)+q^(2))rArr cos ecx+cot x=

int cosec^2 x dx=- cot x

" cosec 2x + cot 2x = cot x "

int_(pi//6)^(pi//2) (" cosec x cot x")/(1+" cosec "^(2) x)dx

int_(pi//6)^(pi//2) (" cosec x cot x")/(1+" cosec "^(2) x)dx

If int (cosec^(2)x)/((cosec x + cot x)^(9/2)) dx = (cosec x - cot x)^(7/2)(1/alpha+((cosec x-cotx)^(2))/11)+C where C is constant of integration and alpha in N) then alpha is