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mojhsa [17]
1 year ago
9

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

Mathematics
1 answer:
Alborosie1 year ago
3 0

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

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