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

The general solution for 2sin^2(x)-cos(x)=0 is x=0.67488…+2pin,x=2pi-0.67488…+2pin

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

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

x = 0.67488 \dots + 2 πn, x = 2 π - 0.67488 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

- cos (x) + (1 - cos^{2} (x)) \cdot 2 = 0

Solve by substitution

cos (x) = - \frac{1 + 17}{4}, cos (x) = \frac{17 - 1}{4}

cos (x) = - \frac{1 + 17}{4} :

No Solution

cos (x) = \frac{17 - 1}{4} : x = arccos (\frac{17 - 1}{4}) + 2 πn, x = 2 π - arccos (\frac{17 - 1}{4}) + 2 πn

Combine all the solutions

x = arccos (\frac{17 - 1}{4}) + 2 πn, x = 2 π - arccos (\frac{17 - 1}{4}) + 2 πn

Show solutions in decimal form

x = 0.67488 \dots + 2 πn, x = 2 π - 0.67488 \dots + 2 πn

3 cos (x) (sin (x) + tan (x)) = 2 (1 + cos (x))

cos (x) = \frac{8.8}{13}

tan^{2} (θ) + 7 tan (θ) + 8 = 0

cos (4 x) = \frac{2}{3}

- 1 + cos (θ) = cos (2 θ)

What is the general solution for 2sin^2(x)-cos(x)=0 ?
The general solution for 2sin^2(x)-cos(x)=0 is x=0.67488…+2pin,x=2pi-0.67488…+2pin