`S=cosecx+cosec 2x+cosec 4x+…+cosec 2nx=cot(x/2)−cot2nx`

Let f(x)= cosec 2x + cosec^(2)2 x+ cosec^(2)3 x+........+ cosec^(2)n ,x in (0,pi/2) and g(x)=f(x)+cot 2^n x . If H(x)={ [(cosx)^(g(x))+(sec)^(cosecx), if x lt 0], [ p, if x=0] ,[ (e^x+e^(-x)-2cosx)/(x sin x), If x lt 0]} .Find the value of p, if possible to make the function H(x) continuous at x = 0 .

int cot^6x cosec^2xdx

f(x)=|(secx,cos x,sec^2x + cot x cosecx),(cos^2x,cos^2x,cosec^2 x),(1,cos^2x,cos^2x)| then int_0^(pi/2) f(x) dx=.....

Solve cot(x//2)-cosec (x//2)=cot x .

int cosec^(2)x. sqrt(cot) dx

Prove the following identities : cosec^(4) A - cosec^(2) A = cot^(4) A + cot^(2) A

Prove that (cosA-sinA+1)/(cosA+sinA-1) =cosec A+ cot A using the identity cosec^(2)A=1+cot^(2)A .

Prove the following identities : (cosec A + sin A) (cosec A - sin A) = cot^(2) A + cos^(2) A

int " cosec"^(4) 2x dx

(cosec A. cosecB+cotA . cotB)^2-(cosec A. cotB + cosecB. cot A)^2 is