What is the general solution for cos(2x)-sin^2(x)-1=3sin(x) ?

The general solution for cos(2x)-sin^2(x)-1=3sin(x) is x=(3pi)/2+2pin,x=2pin,x=pi+2pin

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cos(2x)-sin^2(x)-1=3sin(x)

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

x = \frac{3 π}{2} + 2 πn, x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

3 sin (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = - 1, sin (x) = 0

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn, x = 2 πn, x = π + 2 πn

tan (Θ) = 1.4, 18 0^{\circ} <, Θ < 27 0^{\circ}

(1 + 4 cos (θ))^{2} = (3 sin (θ))

sin (θ) - \frac{cos ( θ )}{5} = 0.6377

cos (2 θ) = 0.4, 0^{\circ} \leq θ \leq 36 0^{\circ}

sin (4 x) = cos (4 x)

What is the general solution for cos(2x)-sin^2(x)-1=3sin(x) ?
The general solution for cos(2x)-sin^2(x)-1=3sin(x) is x=(3pi)/2+2pin,x=2pin,x=pi+2pin