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

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

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

sin^{2} (x) + 2 - 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

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

Subtract

3 sin (x)

from both sides

sin^{2} (x) + 2 - 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

sin^{2} (a) sec (a) = tan^{2} (a)

tan^{2} (θ) - sec (θ) = 1

sin (x) = \frac{8}{10}

sin (x) cos (2 x) + cos (x) sin (2 x) = 0

7 cos (5 x) + 9 = 12

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