Question

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

Answer 1

Answer:

see explanation

Step-by-step explanation:

using the identity

cos2a = 2cos²a - 1 , then

cos2a

= 2[ $\frac{1}{2}$(a  + $\frac{1}{a}$) ]² - 1

= 2 [ $\frac{1}{4}$ (a² + $\frac{1}{a^2}$ + 2) ] - 1

= $\frac{1}{2}$ (a² + $\frac{1}{a^2}$ ) + 1 - 1

= $\frac{1}{2}$ (a² + $\frac{1}{a^2}$ ) ← thus verified