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

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

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

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

x = 2 πn, x = π + 2 πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Factor

2 sin (x) - cos (x) sin (x) : - sin (x) (cos (x) - 2)

2 sin (x) - cos (x) sin (x)

Factor out common term

- sin (x)

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

General solutions for

sin (x) = 0

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

cos (x) - 2 = 0 :

No Solution

cos (x) - 2 = 0

Move

2

to the right side

cos (x) - 2 = 0

Add

2

to both sides

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

Simplify

cos (x) = 2

cos (x) = 2

- 1 \leq cos (x) \leq 1

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

sin (2 x - 20) = - cos (3 x + 50)

\frac{sin ( 6 0 ^{\circ} )}{174.36} = \frac{sin ( x )}{200}

cos (x) = \frac{8}{13}

cos^{2} (4 x) - sin^{2} (4 x) = 0

(3 sin (t)) \cdot (3 cos (t)) = 0

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