What is the general solution for cos^4(2x)-sin^4(2x)=1 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos^4(2x)-sin^4(2x)=1

cos^{4} (2 x) - sin^{4} (2 x) = 1

x = πn, x = \frac{π}{2} + πn

Solution steps

cos^{4} (2 x) - sin^{4} (2 x) = 1

Subtract

1

from both sides

cos^{4} (2 x) - sin^{4} (2 x) - 1 = 0

Apply exponent rule:

a^{b} = a^{2} a^{b - 2}

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

Rewrite using trig identities

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

Divide both sides by

- 2

sin (2 x) = 0

General solutions for

sin (2 x) = 0

2 x = 0 + 2 πn, 2 x = π + 2 πn

Solve

2 x = 0 + 2 πn : x = πn

Solve

2 x = π + 2 πn : x = \frac{π}{2} + πn

x = πn, x = \frac{π}{2} + πn

sin (x) tan (x - 3 0^{\circ}) = 0

- 4 tan^{2} (θ) = - 1

2 cos^{2} (x) + 5 sin (x) + 1 = 0

\frac{125}{sin ( 11 0 ^{\circ} )} = \frac{100}{sin ( b )}

tan (\frac{2 x}{3}) - 3 = 0

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