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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin^3(x)=cos^3(x)

sin^{3} (x) = cos^{3} (x)

x = \frac{π}{4} + πn

Solution steps

sin^{3} (x) = cos^{3} (x)

Subtract

cos^{3} (x)

from both sides

sin^{3} (x) - cos^{3} (x) = 0

Factor

sin^{3} (x) - cos^{3} (x) : (sin (x) - cos (x)) (sin^{2} (x) + sin (x) cos (x) + cos^{2} (x))

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

Rewrite using trig identities

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

Solving each part separately

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

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

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

No Solution

Combine all the solutions

x = \frac{π}{4} + πn

2 sin (θ) = 3 cos (θ) - 1, 0 <, θ < 360

cot (2 θ) + csc (2 θ) - 7 = 0

sec (x) sin (x) + cos (x) = sec (x)

0 = 2 + 2 sin (θ)

x, 2 cos (x) + 3 = 0

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