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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = - \frac{3}{2}, sin (x) = 0

sin (x) = - \frac{3}{2} :

No Solution

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

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

cos (x) = 3 sin (x)

tan (23 θ) + cot (23 θ) = \frac{4}{3}

tan^{2} (x) + 1 = sec (x)

\frac{3}{16} = 1 (cos (0)) (cos (3 0^{\circ})) (cos (x - 3 0^{\circ}))

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