What is the general solution for 3sin(x)=2cos^2(x) ?

The general solution for 3sin(x)=2cos^2(x) is x= pi/6+2pin,x=(5pi)/6+2pin

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3sin(x)=2cos^2(x)

3 sin (x) = 2 cos^{2} (x)

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

3 sin (x) = 2 cos^{2} (x)

Subtract

2 cos^{2} (x)

from both sides

3 sin (x) - 2 cos^{2} (x) = 0

Rewrite using trig identities

- (1 - sin^{2} (x)) \cdot 2 + 3 sin (x) = 0

Solve by substitution

sin (x) = \frac{1}{2}, sin (x) = - 2

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = - 2 :

No Solution

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin^{2} (x) - sin (x) - 2 = 0

tan (x) - 3 = 0

cos^{2} (θ) - sin^{2} (θ) = 1 - sin (θ)

sin (x) cos (x) = \frac{2}{4}

cos^{2} (x) = 1 + sin (x)

What is the general solution for 3sin(x)=2cos^2(x) ?
The general solution for 3sin(x)=2cos^2(x) is x= pi/6+2pin,x=(5pi)/6+2pin