Number of values that satisfy 2\sin^2(x)-3=3\cos(x),\ 90^\circ<x<270^\circ

kabutjv7

kabutjv7

Answered question

2022-04-24

Number of values that satisfy
2sin2(x)3=3cos(x), 90<x<270

Answer & Explanation

Volsa280

Volsa280

Beginner2022-04-25Added 16 answers

2sin2(x)3=3cos(x)2(1cos2(x))3=3cos(x)
2cos2(x)+3cos(x)+1=0(cos(x)+1)(2cos(x)+1)=0
So we can say cos(x)=1 or cos(x)=12
cos(x)=1x=2kπ+πx=π
cos(x)=12x=2π3 and x=4π3
So totally there are three different values for x, satisfying the mentioned equation in the intended interval.

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