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

The general solution for sin^2(x)=2cos(x) is x=1.14371…+2pin,x=2pi-1.14371…+2pin

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

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

x = 1.14371 \dots + 2 πn, x = 2 π - 1.14371 \dots + 2 πn

Solution steps

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

Subtract

2 cos (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = - 1 - 2, cos (x) = 2 - 1

cos (x) = - 1 - 2 :

No Solution

cos (x) = 2 - 1 : x = arccos (2 - 1) + 2 πn, x = 2 π - arccos (2 - 1) + 2 πn

Combine all the solutions

x = arccos (2 - 1) + 2 πn, x = 2 π - arccos (2 - 1) + 2 πn

Show solutions in decimal form

x = 1.14371 \dots + 2 πn, x = 2 π - 1.14371 \dots + 2 πn

2 cos^{2} (θ) + 4 sin (θ) - 13 = 9 sin (θ) - 9

cot (θ) = - \frac{5}{4}

tan^{2} (θ) + 5 tan (θ) = 0

sin (4 x) - sin (6 x) = 0

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

What is the general solution for sin^2(x)=2cos(x) ?
The general solution for sin^2(x)=2cos(x) is x=1.14371…+2pin,x=2pi-1.14371…+2pin