What is the general solution for (sin(2x))/(sin(x))=1.5 ?

The general solution for (sin(2x))/(sin(x))=1.5 is x=0.72273…+2pin,x=2pi-0.72273…+2pin

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(sin(2x))/(sin(x))=1.5

\frac{sin ( 2 x )}{sin ( x )} = 1.5

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

Solution steps

\frac{sin ( 2 x )}{sin ( x )} = 1.5

Subtract

1.5

from both sides

\frac{sin ( 2 x )}{sin ( x )} - 1.5 = 0

Rewrite using trig identities

- 1.5 + 2 cos (x) = 0

Move

1.5

to the right side

2 cos (x) = 1.5

Divide both sides by

2

cos (x) = 0.75

Apply trig inverse properties

x = arccos (0.75) + 2 πn, x = 2 π - arccos (0.75) + 2 πn

Show solutions in decimal form

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

x, yz = sin (x y)

sin^{2} (x) = \frac{( 5 m - 5 )}{2}

2 cot (2 x) = 4

cos (θ) = \frac{4}{3.3 8 ^{2} + 2 ^{2}}

23 sin (2 θ) = 3

What is the general solution for (sin(2x))/(sin(x))=1.5 ?
The general solution for (sin(2x))/(sin(x))=1.5 is x=0.72273…+2pin,x=2pi-0.72273…+2pin