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# if  `sin^(2) theta + sin^(2) 2theta + sin^(2) 3 theta= 1` what does  `cos^(2) 3 theta...

aba111 | eNoter

Posted July 14, 2013 at 8:45 PM via web

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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?

Tagged with help, math, trigonometry

### 1 Answer |

degeneratecircle | High School Teacher | (Level 2) Associate Educator

Posted July 14, 2013 at 11:43 PM (Answer #1)

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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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