What is cos^4(x)-sin^4(x) ?

The solution to cos^4(x)-sin^4(x) is cos(2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify cos^4(x)-sin^4(x)

simplify

cos^{4} (x) - sin^{4} (x)

cos (2 x)

Solution steps

cos^{4} (x) - sin^{4} (x)

Factor

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

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

Rewrite using trig identities

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

Expand

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

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

Rewrite using trig identities

= cos (2 x)

2 \frac{1}{4} \div 2

(5 + i) (8 - i)

2 (10 x + 3)^{3}

654

- \frac{3}{5} \times 5