What is (cos^4(x)-sin^4(x))/(cos^2(x)-sin^2(x)) ?

The solution to (cos^4(x)-sin^4(x))/(cos^2(x)-sin^2(x)) is 1

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simplify (cos^4(x)-sin^4(x))/(cos^2(x)-sin^2(x))

simplify

\frac{cos ^{4} ( x ) - sin ^{4} ( x )}{cos ^{2} ( x ) - sin ^{2} ( x )}

1

Solution steps

\frac{cos ^{4} ( x ) - sin ^{4} ( x )}{cos ^{2} ( x ) - sin ^{2} ( x )}

Factor

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

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

Cancel the common factor:

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

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

Use the Pythagorean identity:

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

= 1

det (2 a^{- 1} b)

(2 x - 2)^{- 3}

(\frac{( 3 + 2 ) a}{3})^{2}

(1 + a)^{2} (1 + b^{2}) - (1 + b)^{2} (1 + a^{2})

(\frac{1}{2})^{- 2 t}

What is (cos^4(x)-sin^4(x))/(cos^2(x)-sin^2(x)) ?
The solution to (cos^4(x)-sin^4(x))/(cos^2(x)-sin^2(x)) is 1