Question

If cosa=1/2(a+1/a), verify that. cos2a=1/2(a²+1/a²)​

Answer 1

see explanation

Explanation:

using the identity

cos2a = 2cos²a - 1 , then

cos2a

= 2[
`(1)/(2)`(a +
`(1)/(a)`) ]² - 1

= 2 [
`(1)/(4)` (a² +
`(1)/(a^2)` + 2) ] - 1

=
`(1)/(2)` (a² +
`(1)/(a^2)` ) + 1 - 1

=
`(1)/(2)` (a² +
`(1)/(a^2)` ) ← thus verified