Let `f(x)=(2cosx-1)(2cos2x-1)(2cos2^2x-1).... (2cos2^(n-1) x-1),` (where `ngeq1)dot` Then prove that `f((2pik)/(2^n+-1))=1AAk in Idot`

sin^(-1)(2cos^(2)x-1)+cos^(-1)(1-2sin^(2)x)=

Prove that cos^(-1){(1+x)/2}=(cos^(-1)x)/2

If f(x)=log[(1+x)/(1-x)], then prove that f[(2x)/(1+x^2)]=2f(x)dot

If f(x)=(h_1(x)-h_1(-x))(h_2(x)-h_2(-x))... (h_(2n+1)(x)-h_(2n+1)(-x)a n df(200)=0, then prove that f(x) is many one function.

If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

Let f(x)=cos(a_1+x)+1/2cos(a_2+x)+1/(2^2)cos(a_1+x)++1/(2^(n-1))cos(a_n+x) where a)1,a_2 a_n in Rdot If f(x_1)=f(x_2)=0,t h e n|x_2-x_1| may be equal to pi (b) 2pi (c) 3pi (d) pi/2

Let f(x)=sin^(-1)((2x)/(1+x^(2))) and g(x)=cos^(-1)((x^(2)-1)/(x^(2)+1)) . Then tha value of f(10)-g(100) is equal to

Prove that cos A cos 2A cos 2^(2) A cos 2^(3)A....cos 2^(n-1) A=(sin 2^(n) A)/(2^(n) sin A)

If cos^(-1) x + cos^(-1) y + cos ^(-1) z = pi and 0 lt x,y,z lt 1 show that x^(2) +y^(2) +z^(2) +2xyz = 1