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

The general solution for cos(2x)-2sin(x)=0 is x=0.37473…+2pin,x=pi-0.37473…+2pin

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

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

x = 0.37473 \dots + 2 πn, x = π - 0.37473 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = - \frac{1 + 3}{2}, sin (x) = \frac{3 - 1}{2}

sin (x) = - \frac{1 + 3}{2} :

No Solution

sin (x) = \frac{3 - 1}{2} : x = arcsin (\frac{3 - 1}{2}) + 2 πn, x = π - arcsin (\frac{3 - 1}{2}) + 2 πn

Combine all the solutions

x = arcsin (\frac{3 - 1}{2}) + 2 πn, x = π - arcsin (\frac{3 - 1}{2}) + 2 πn

Show solutions in decimal form

x = 0.37473 \dots + 2 πn, x = π - 0.37473 \dots + 2 πn

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

2 sin (x) + 53 = 63

- 5 \cdot cos (x) - 8.6602500000000 \dots \cdot sin (x) = - 5

y, cos (x) + cos (y) + cos (z) = 0

cos (x) = \frac{2}{5}

What is the general solution for cos(2x)-2sin(x)=0 ?
The general solution for cos(2x)-2sin(x)=0 is x=0.37473…+2pin,x=pi-0.37473…+2pin