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

The general solution for 2cos^2(x)-sin^2(x)-2sin(x)=0 is x=0.58066…+2pin,x=pi-0.58066…+2pin

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

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

x = 0.58066 \dots + 2 πn, x = π - 0.58066 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = - \frac{1 + 7}{3}, sin (x) = \frac{7 - 1}{3}

sin (x) = - \frac{1 + 7}{3} :

No Solution

sin (x) = \frac{7 - 1}{3} : x = arcsin (\frac{7 - 1}{3}) + 2 πn, x = π - arcsin (\frac{7 - 1}{3}) + 2 πn

Combine all the solutions

x = arcsin (\frac{7 - 1}{3}) + 2 πn, x = π - arcsin (\frac{7 - 1}{3}) + 2 πn

Show solutions in decimal form

x = 0.58066 \dots + 2 πn, x = π - 0.58066 \dots + 2 πn

cos^{2} (x) + 5 cos (x) - 2 = 0

cos (2 x) + cos (2 x) + 1 = 0

(cos^{2} (x) + cos (x)) \cdot (sin (x) + sin^{3} (x)) = 0

arccos (x) - arcsin (x) = arcsin (1 - x)

sin^{2} (x) = ∣ sin (x) ∣

What is the general solution for 2cos^2(x)-sin^2(x)-2sin(x)=0 ?
The general solution for 2cos^2(x)-sin^2(x)-2sin(x)=0 is x=0.58066…+2pin,x=pi-0.58066…+2pin