Solve trigonometric equation \(\displaystyle{\sin{{14}}}{x}-{\sin{{12}}}{x}+{8}{\sin{{x}}}-{\cos{{13}}}{x}={4}\)

Nathen Peterson

Nathen Peterson

Answered question

2022-03-22

Solve trigonometric equation sin14xsin12x+8sinxcos13x=4

Answer & Explanation

Avery Maxwell

Avery Maxwell

Beginner2022-03-23Added 13 answers

We can use sinxsiny=2sinxy2cosx+y2. So
(sin14xsin12)+8sinxcos13x=4
2sinxcos13xcos13x+8sinx4=0
2cos13x(sinx12)+8(sinx12)=0
(sinx12)(2cos13x+8)=0
So, we have sinx=12 and cos13x=4 (which can't be achieved), now we take just sinx=12, and we get x1=π6, x2=5π6 on the given interval.

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