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

The general solution for 0=-2sin(x)+2cos(2x) is x=(3pi)/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

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

Switch sides

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

Rewrite using trig identities

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

Solve by substitution

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

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

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

9 cos (x) + 9 sin (x) tan (x) = 18

cot (2 x) = 1

5 tan^{2} (x) - 15 = 0

- 2 cos^{2} (x) = - cos (x) - 1

sin (θ) = - \frac{2}{5}

What is the general solution for 0=-2sin(x)+2cos(2x) ?
The general solution for 0=-2sin(x)+2cos(2x) is x=(3pi)/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin