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

The general solution for cos(x)-sin(-x)=0 is x=(3pi)/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{3 π}{4} + πn

Degrees

x = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

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

Simplify

cos (x) - (- sin (x)) : cos (x) + sin (x)

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

Apply rule

- (- a) = a

= cos (x) + sin (x)

cos (x) + sin (x) = 0

Divide both sides by

cos (x), cos (x) \neq = 0

\frac{cos ( x ) + sin ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

1 + \frac{sin ( x )}{cos ( x )} = 0

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

1 + tan (x) = 0

1 + tan (x) = 0

Move

1

to the right side

1 + tan (x) = 0

Subtract

1

from both sides

1 + tan (x) - 1 = 0 - 1

Simplify

tan (x) = - 1

tan (x) = - 1

General solutions for

tan (x) = - 1

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

- 4 cos (x) = 0

7 cos^{2} (θ) - 3 = - 2 cos (θ) + 2

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

sin^{2} (θ) + sin (θ) - 6 = 0

y, x + tan (x y) = 0

What is the general solution for cos(x)-sin(-x)=0 ?
The general solution for cos(x)-sin(-x)=0 is x=(3pi)/4+pin