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

The general solution for cos^2(x)-2sin(x)=0 is x=0.42707…+2pin,x=pi-0.42707…+2pin

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

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

x = 0.42707 \dots + 2 πn, x = π - 0.42707 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

sin (x) = - 1 - 2 :

No Solution

sin (x) = 2 - 1 : x = arcsin (2 - 1) + 2 πn, x = π - arcsin (2 - 1) + 2 πn

Combine all the solutions

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

Show solutions in decimal form

x = 0.42707 \dots + 2 πn, x = π - 0.42707 \dots + 2 πn

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

sin (3 x) - 3 sin (x) = 0

sin (x) = \frac{2.1}{4}

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

sin (x) = 0, 5

What is the general solution for cos^2(x)-2sin(x)=0 ?
The general solution for cos^2(x)-2sin(x)=0 is x=0.42707…+2pin,x=pi-0.42707…+2pin