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

The general solution for sin^2(x)-2cos(x)=0 is x=1.14371…+2pin,x=2pi-1.14371…+2pin

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

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

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

Solution steps

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

3 sin^{2} (θ) + 3 sin (θ) - 6 = - 4 sin (θ)

sin (4 x) - cos (3 x) = sin (2 x)

sin (x) cos (x) = \frac{1}{2} tan (x)

x, 2 sec^{2} (x) + tan^{2} (x) - 3 = 0

5 sin (\frac{θ}{2}) = 5 cos (\frac{θ}{2})

What is the general solution for sin^2(x)-2cos(x)=0 ?
The general solution for sin^2(x)-2cos(x)=0 is x=1.14371…+2pin,x=2pi-1.14371…+2pin