What is sin^4(θ)-cos^4(θ) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify sin^4(θ)-cos^4(θ)

simplify

sin^{4} (θ) - cos^{4} (θ)

- cos (2 θ)

Solution steps

sin^{4} (θ) - cos^{4} (θ)

Factor

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

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

Rewrite using trig identities

= (- cos (θ) + sin (θ)) (cos (θ) + sin (θ))

Expand

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

= - cos^{2} (θ) + sin^{2} (θ)

Rewrite using trig identities

= - cos (2 θ)

x^{2} + 15 x + 14

\frac{1 0 ^{3} \cdot 10 0 ^{2} \cdot 100 0 ^{4}}{( 1 0 ^{2} ) ^{5} \cdot 100}

\frac{- 4 + 8 i}{- 6 i}

x^{8} - 81 y^{8}