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

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

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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)

\frac{55}{6 ( 3 - 2 ) + 5} + \frac{2 ( 3 ) ^{2}}{8 - 2}

318 - 212 + 32

\frac{( 4 \cdot 3 ^{22} + 7 \cdot 3 ^{21} ) \cdot 57}{( 19 \cdot 2 7 ^{4} ) ^{2}}

\frac{( x ^{2} y ^{- 3} ) ^{\frac{1}{4}}}{x ^{- 1} y ^{2}}

\frac{cot ( x )}{csc ( x )}