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

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

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

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

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

Solution steps

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

Subtract

2 sin (x)

from both sides

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^{4} (θ) + cos^{4} (θ) = 2 sin^{2} (θ) - 1

x, \frac{- y}{2} + sin (x) = 0

cos (a) = 0.33

tan (θ) = \frac{3}{- 2}

4 sin^{2} (r) - sin (r) = 0

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