IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

harsha_27

Let f(x) = (2cosx-1)(2cos2x-1)(2cos4x-1)..........(2cos32x-1) , then f(2

/13) is

(A)-1

(B) 1

(C)1/2

(D)None of these

Answer:(B)

Please explain the solution.

lokeshsardana

2cos2x - 1 = 2(2cos²x - 1) - 1

= cos3x/cosx

//ly we can write for other

so, f(x) =

{cos3/2x.cos3x.cos6x.........cos48x}/{cosx/2.cosx.cos2x............cos16x}

= sin(2⁵.3x).sin(x/2)/{sin3x/2.sin2⁵x}

put x = 2pi/13

= sin(10pi/13).sin(pi/13)/{sin(3pi/13).sin(12pi/13)}

= 1

because sin(10pi/13)= sin(3pi/13)

and sin(pi/13) = sin(12pi/13)

iitkgp_bipin

That's a perfect solution. Great work Lokesh.

lokeshsardana

thanx bro....................