Solve this trigonometric equation \sin 2x- \sqrt3 \cos 2x=2 I tried

Dowqueuestbew1j 2021-12-27 Answered
Solve this trigonometric equation sin2x3cos2x=2
I tried dividing both sides with cos2x but then I win 2cos2x
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Expert Answer

sukljama2
Answered 2021-12-28 Author has 33 answers
12sin2x32cos2x=1
sin2xcosπ3cos2xsinπ3=1
sin(2xπ3)=1
I hope you can solve further.
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abonirali59
Answered 2021-12-29 Author has 35 answers
MySolution:: Given sin2x3cos2x=2
We can write it as
sin2x12cos2x32=1sin(2xπ3)=1=sinπ2
Above we have used the formula
sinαcosβcosαsinβ=sin(αβ)
So
2xπ3=nπ+(1)nπ2x=nπ2+(1)nπ4+π6
Where nZ
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nick1337
Answered 2022-01-08 Author has 510 answers

Divide by 2 to get
1=12sin(2x)32cos(2x)
then find an angle y for which cosy=12 and siny=32 and remember that
sin(ab)=sinacosbcosasinb

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