What is the general solution for 4sin^2(x)-cos(x)-1=0 ?

The general solution for 4sin^2(x)-cos(x)-1=0 is x=pi+2pin,x=0.72273…+2pin,x=2pi-0.72273…+2pin

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4sin^2(x)-cos(x)-1=0

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

x = π + 2 πn, x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = - 1, cos (x) = \frac{3}{4}

cos (x) = - 1 : x = π + 2 πn

cos (x) = \frac{3}{4} : x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

Combine all the solutions

x = π + 2 πn, x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

Show solutions in decimal form

x = π + 2 πn, x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

tan (\frac{θ}{2} - \frac{π}{4}) = 1, 0 \leq θ < 2 π

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

2 sin^{2} (x) + sin (x) - 6 = 0

tan (θ) = \frac{8}{15}, sin (θ) > 0

cos (x) = \frac{86.6}{100}

What is the general solution for 4sin^2(x)-cos(x)-1=0 ?
The general solution for 4sin^2(x)-cos(x)-1=0 is x=pi+2pin,x=0.72273…+2pin,x=2pi-0.72273…+2pin