What is expand (1+tan(α)tan(β))tan(α-β) ?

The solution to expand (1+tan(α)tan(β))tan(α-β) is tan(α-β)+tan(α-β)tan(α)tan(β)

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expand (1+tan(α)tan(β))tan(α-β)

expand

(1 + tan (α) tan (β)) tan (α - β)

tan (α - β) + tan (α - β) tan (α) tan (β)

Solution steps

(1 + tan (α) tan (β)) tan (α - β)

= tan (α - β) (1 + tan (α) tan (β))

Apply the distributive law:

a (b + c) = ab + a c

tan (α - β) (1 + tan (α) tan (β)) = tan (α - β) \cdot 1 + tan (α - β) tan (α) tan (β)

= tan (α - β) \cdot 1 + tan (α - β) tan (α) tan (β)

Apply rule:

a \cdot 1 = a

tan (α - β) \cdot 1 = tan (α - β)

= tan (α - β) + tan (α - β) tan (α) tan (β)

\frac{( x ^{2} + 1 ) ( x ^{4} + 1 ) ( x ^{6} + 1 )}{x ^{6}}

\frac{1}{n ( n + 1 ) ( n + 2 )}

(sec (x) - 1)^{2}

(x + 2 i)^{2}

\frac{1}{x ^{3}} (\frac{1}{3 x ^{2}} - \frac{x}{2})^{9}

What is expand (1+tan(α)tan(β))tan(α-β) ?
The solution to expand (1+tan(α)tan(β))tan(α-β) is tan(α-β)+tan(α-β)tan(α)tan(β)