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

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

simplify

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

- cos (2 x)

Solution steps

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

Factor

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

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

Rewrite using trig identities

= - cos (2 x)

(42)^{2}

40 \times 5

(5 - 6 i) + (9 + 9 i)

- \frac{1}{2} \times 1

(p + q)^{3}