x के सापेक्ष समाकलन कीजिए -
`sin^(n)(sin^(-1)x)`

int sin^(n)(sin^(-1)x)dx

Show that int sin^(n)xdx=(-sin^(n-1)x*cos x)/(n)+(n-1)/(n)int sin^(n-2)ndx also find int sin^(6)dx

sin x + sin2x + sin3x + ... + sin nx = (sin ((n + 1) / (2)) x (sin (nx)) / (2)) / (sin ((x) / (2)) )

Letf(x) = lim_( n to oo) (x^(n)-sin x^(n))/(x^(n)+sin x^(n)) " for" xgt 0, x ne 1,and f(1)=0 Discuss the continuity at x=1.

sin^(-1)[sqrt(x^(2)-x^(3))-sqrt(x-x^(3))]=..... a) sin^(-1)x+sin^(-1)sqrt(x) b) sin^(-1)x-sin^(-1)sqrt(x) c) sin^(-1)sqrt(x)-sin^(-1)x d) 2sin^(-1)x

Prove that: s in x+s in3x++sin(2n-1)x=(sin^(2)nx)/(s in x) for all n in N.

If sin x + "cosec"x=2 , then, for all n in N , the value of: sin^(n)x + "cosec"^(n)x=

Prove that nC_ (1) sin x * cos (n-1) x + nC_ (2) sin2x * cos (n-2) x + nC_ (3) sin3x * cos (n-3) x + ... + nC_ ( n) sin nx = 2 ^ (n-1) sin nn