Problem in finding the General Solution of a Trigonometric Equation v3

[Wrichik Basu]

Homework Statement

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

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

Homework Equations

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These equations may help:

The Attempt at a Solution

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Please see the pic below:

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

 

[BvU]

Is there really a difference ?

 

[Wrichik Basu]

Is there really a difference ?

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

 

[BvU]

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

 

[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.

 

[BvU]

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.

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

 

[Wrichik Basu]

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.

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

understood. Thank you.

 

[scottdave]

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

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