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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(x)=1-sin(x)

cos (x) = 1 - sin (x)

x = 2 πn, x = 2 πn + \frac{π}{2}

Solution steps

cos (x) = 1 - sin (x)

Subtract

1 - sin (x)

from both sides

cos (x) - 1 + sin (x) = 0

Rewrite using trig identities

- 1 + 2 sin (x + \frac{π}{4}) = 0

Move

1

to the right side

2 sin (x + \frac{π}{4}) = 1

Divide both sides by

2

sin (x + \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (x + \frac{π}{4}) = \frac{2}{2}

x + \frac{π}{4} = \frac{π}{4} + 2 πn, x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

Solve

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

Solve

x + \frac{π}{4} = \frac{3 π}{4} + 2 πn : x = 2 πn + \frac{π}{2}

x = 2 πn, x = 2 πn + \frac{π}{2}

2 sin (2 θ) = cos (2 θ), 0 \leq θ \leq 2 π

tan (4 x) - 1 = 0

\frac{cos ( x ) cot ( x )}{1 - sin ( x )} = 3

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

tan^{2} (x) = - 1 + 2 tan (- x)

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