What is the general solution for 4sin(x)-3sin^2(x)+cos^2(x)-2=0 ?

The general solution for 4sin(x)-3sin^2(x)+cos^2(x)-2=0 is x= pi/6+2pin,x=(5pi)/6+2pin

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4sin(x)-3sin^2(x)+cos^2(x)-2=0

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

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

Solution steps

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

Rewrite using trig identities

- 1 + 4 sin (x) - 4 sin^{2} (x) = 0

Solve by substitution

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

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}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

cos^{2} (x) + 3 cos (x) = 1

cot^{2} (x) = \frac{tan ( x )}{2}

tan (θ) = \frac{3.2}{4.1}

5 sec (x) tan (x) = 0

cos (5 x) - cos (x) = 2 sin (2 x)

What is the general solution for 4sin(x)-3sin^2(x)+cos^2(x)-2=0 ?
The general solution for 4sin(x)-3sin^2(x)+cos^2(x)-2=0 is x= pi/6+2pin,x=(5pi)/6+2pin