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

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

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

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

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

Solution steps

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

Subtract

3 sin (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

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

Combine all the solutions

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

y, x tan (y) - x^{2} sin (x) + 3 x^{3} = 0

(\frac{( 1 - sin ^{2} ( x ) )}{( 1 + 2 \cdot sin ^{2} ( x ) )}) = 0.45

- 5 sin (t) = 0

4 cos (\frac{θ}{2}) = 3 + 2 cos (θ)

tan (θ + 1 0^{\circ}) = cot (2 θ - 10)

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