What is expand 1/2 cot(4x)(1-tan^2(4x)) ?

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

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expand 1/2 cot(4x)(1-tan^2(4x))

expand

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

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

Solution steps

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

Apply the distributive law:

a (b - c) = ab - a c

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

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

Simplify

\frac{1}{2} cot (4 x) \cdot 1 - \frac{1}{2} cot (4 x) tan^{2} (4 x) : \frac{cot ( 4 x ) - cot ( 4 x ) tan ^{2} ( 4 x )}{2}

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

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