What is the general solution for 3sin(x)+cos(2x)=2 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3sin(x)+cos(2x)=2

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

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

Solution steps

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

Subtract

2

from both sides

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

Rewrite using trig identities

- 1 - 2 sin^{2} (x) + 3 sin (x) = 0

Solve by substitution

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

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

cos (3 x) + cos (5 x) = cos (x)

sin (θ) + sin (θ) cos (θ) = 0

8 + 4 cos (2 x) = 12 cos (x)

tan (x) = - sec (x)

3 tan^{4} (θ) + 1 = \frac{2}{tan ^{2} ( θ )}

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