Question

If 2sin^2x=3cosx find x

Answer 1

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Answer 2

Answer:

If you are looking for answers within [0,2pi); x=0, 2pi/3 and 4pi/3

Step-by-step explanation:

2sin^2(x)=3cos(x), subtract 3cos(x) from both sides

2sin^2(x)-3cos(x)=0, divide all terms by 2

sin^2(x)-3/2cos(x)=0, use the trig identity sin^2(x)=1-cos^2(x) to replace sin^2(x)

1-cos^2(x)-3/2cos(x)=0, Factor out cos(x) and subtract 1 from both sides

-cos(x)(cos(x)+3/2)=-1, Divide by -1

cos(x)(cos(x)+3/2)=1, Solve for x;

cos(x)=1  or  cos(x)+3/2=1

x=0,2pi (0+2pi*kez) or cos(x)=-1/2, x=2pi/3 or 4pi/3 (2pi/3+2pi*kez) or (4pi/3+2pi*kez)