What is ((1-cos^4(x)))/((tan(x)-cot(x))) ?

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

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simplify ((1-cos^4(x)))/((tan(x)-cot(x)))

simplify

\frac{( 1 - cos ^{4} ( x ) )}{( tan ( x ) - cot ( x ) )}

- \frac{1 - cos ^{4} ( x )}{2 cot ( 2 x )}

Solution steps

\frac{1 - cos ^{4} ( x )}{tan ( x ) - cot ( x )}

Simplify

tan (x) - cot (x) : - 2 cot (2 x)

= \frac{1 - cos ^{4} ( x )}{- 2 cot ( 2 x )}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{1 - cos ^{4} ( x )}{2 cot ( 2 x )}

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

x^{2} + (x + 1) 2

4 a^{2} - 16 b^{2}

n + 2 m^{2} + 1 + 2 m^{2} n

\frac{( x ^{n + 1} + x ^{n - 1} )}{( x ^{2} + 1 )}

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