Period of `cosec(x+x/2+x/4+x/8+...oo)`

Period of cosec (x+(x)/(2) + (x)/(4)+…) is

The period of "cosec"(6-5x) is

The period of (cos (3 x+ 4) + tan (5x+7))/( cosec (3+4x) - sin(4-6x) is

intcot^3x cosec^4x dx

Given that cos(x/2).cos(x/4).cos(x/8)..... = sinx/x Prove that (1/2^2)sec^2(x/2) +(1/2^4)sec^2(x/4) +..... = cosec^2x - 1/(x^2)

Draw the graph of y = " cosec "^(2) x - cot^(2) x. Is f(x) periodic ? If yes, what is its fundamental period ?

Draw the graph of y = " cosec "^(2) x - cot^(2) x. Is f(x) periodic ? If yes, what is its fundamental period ?

Draw the graph of y = " cosec "^(2) x - cot^(2) x. Is f(x) periodic ? If yes, what is its fundamental period ?