What is the general solution for 2cos(2x)-1=1-2sin(2x) ?

The general solution for 2cos(2x)-1=1-2sin(2x) is x=2pin,x=pi+2pin,x= pi/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2cos(2x)-1=1-2sin(2x)

2 cos (2 x) - 1 = 1 - 2 sin (2 x)

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn

Solution steps

2 cos (2 x) - 1 = 1 - 2 sin (2 x)

Subtract

1 - 2 sin (2 x)

from both sides

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

Rewrite using trig identities

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

Factor

- 4 sin^{2} (x) + 4 cos (x) sin (x) : 4 sin (x) (- sin (x) + cos (x))

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

- sin (x) + cos (x) = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn

cot^{2} (θ) + 3 csc (θ) = - 3

3 tan^{2} (α) = 3 tan (α)

cos (4 x) + cos (2 x) = 0

sin (x) = \frac{10}{50}

6 sin (4 x) + 4 = 5, 0 \leq x \leq 2 π

What is the general solution for 2cos(2x)-1=1-2sin(2x) ?
The general solution for 2cos(2x)-1=1-2sin(2x) is x=2pin,x=pi+2pin,x= pi/4+pin