Question

if 2cos y=x+1/x, prove that cos2y =1/2 (x2 +1/x2)​

Answer 1

Answer:

it is true that the only one

Answer 2

Answer:

2cosa = x + 1/x

We need prove that :

2cos3x = x^3 + 1/x^3

We know that:

cos3a = 4cos^3 a - 3cos a

Now multiply by 2:

2cos3a = 8cos^3 a - 6cos a

= (2cos a)^3 - 3*2cos a

But 2cos a = x + 1/x

==> 2cos3x = (x+ 1/x)^3 - 3(x+1/x)

Open brackets:

==> 2cos3a= x^3 + 3x^2(1/x) + 3x(1/x^2) + 1/x^3 - 3(x + 1/x)

x^3 + 3x + 3/x + 1/x^3 - 3x - 3/x

Now r3educe similar:

==> cos 3a = x^3 + 1/x^3