What is the general solution for 6sin(x)-3sin^2(x)=3-cos^2(x) ?

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

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6sin(x)-3sin^2(x)=3-cos^2(x)

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

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

Solution steps

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

Subtract

3 - cos^{2} (x)

from both sides

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

Rewrite using trig identities

- 2 - 4 sin^{2} (x) + 6 sin (x) = 0

Solve by substitution

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

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

1 - tan^{2} (x) = a^{2} + b^{2}

4 sin (x) - 4 sin^{3} (x) = 0

5 tan^{4} (x) - 10 tan^{2} (x) + 1 = 0

6 tan (x) = 8

sin (x) cos (x - 6 0^{\circ}) = 0

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