`sin x+sin 2x + sin 3x+...+ sin nx =(sin((n+1)/2)xsin(nx)/2)/sin(x/2)`

For all ninNN , prove by principle of mathematical induction that, sinx+sin2x+sin3x+ . . . +sinnx=("sin"(n+1)/(2)x"sin"(nx)/(2))/("sin"(x)/(2))

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

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

If y=sin x*sin2x.sin3x......sin nx, find y'

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

(sin x) / (sin2x sin3x) + (sin x) / (sin3x sin4x) + (sin x) / (sin4x sin5x) + .... n

Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x )

If f(x) = |(sin x + sin 2x + sin 3x, sin 2x , sin 3x),(3 + 4 sin x, 3, 4 sin x),(1 + sin x, sin x, 1)| then the value of int_0^(-pi//2) f(x) dx equals :

For all ninNN , prove by principle of mathematical induction that, sinx+sin3x+ . . .+sin(2n-1)x=(sin^(2)nx)/(sinx)