Problem in finding the General Solution of a Trigonometric Equation v3

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1. May 19, 2017

Wrichik Basu

1. The problem statement, all variables and given/known data:

Find the general solution of the Trigonometric equation: $$3\sin ^2 {\theta} + 7\cos ^2 {\theta} =6$$

Given andwer: $n\pi \pm \frac {\pi}{6}$

2. Relevant equations:

These equations may help:

3. The attempt at a solution:

Please see the pic below:

It seems correct from my side, but the answer is not matching.

2. May 19, 2017

BvU

Is there really a difference ?

3. May 19, 2017

Wrichik Basu

Couldn't understand.... could you explain a bit...

4. May 19, 2017

BvU

Fill in n = 1, 2, 3 in both expressions (yours and the book one)

5. May 19, 2017

scottdave

There is a pi radian difference between -pi/6 and 5pi/6, same with pi/6 and -5pi/6. So you can just say it is +-pi/6 + n*pi, where n can be any integer. That covers all of your scenarios.

6. May 19, 2017

BvU

Why don't you let Wrichik make that discovery himself ?

7. May 19, 2017

Wrichik Basu

understood. Thank you.

8. May 19, 2017

scottdave

Thanks. I guess I didn't see your response about plugging in 1,2,3, etc when I wrote my suggestion.

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