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

If f(x) = cos(x)cos(2x)cos(2^(2)x)…cos(2^(n-1)x) and n gt1 , then f'((pi)/(2)) is

Let f(x) = |{:(cos x ,1,0 ),(1,2cosx,1),(0,1,2cosx):}| then

f(x)=cos^(-1)(x^(2)/sqrt(1+x^(2)))

If f(x) = cos x\ cos 2x\ cos 2^2\ x\ cos 2^3 x\ ....cos2^(n-1) x and n gt 1, then f'(pi/2) is

To prove (cos5x+cos4x)/(1-2cos3x) = -cos2x-cosx

If f(x)=cos^(-1)(2x^(2)-1), x in [-1,1]. Then

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi , prove that x^(2)+y^(2)+z^(2)+2xyz=1

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)=cos(a_1+x)+1/2cos(a_2+x)+1/(2^2)cos(a_3+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 (a) pi (b) 2pi (c) 3pi (d) pi/2

If cos^(-1) x + cos^(-1) y + cos^(-1) z = pi , prove that x^(2) + y^(2) + z^(2) + 2xyz = 1