if `sin^(2) theta + sin^(2) 2theta + sin^(2) 3 theta= 1`

what does

`cos^(2) 3 theta + cos^(2) 2 theta + cos^(2) theta`

equal?

### 1 Answer | Add Yours

For any value of `theta,`

`sin^2 theta+cos^2 theta=1` (1)

`sin^2 2theta+cos^2 2theta=1` (2)

`sin^2 3theta+cos^2 3theta=1` (3)

Thus, if we add equations (1), (2), and (3), we get`sin^2 theta+sin^2 2theta+sin^2 3theta`

`+cos^2 theta+cos^2 2theta+cos^2 3theta=3.`

It is given that `sin^2 theta+sin^2 2theta+sin^2 3theta=1,` **so we must have** `cos^2 theta+cos^2 2theta+cos^2 3theta=2.`

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