What is expand (sec(x)tan(x))(tan(x)-1) ?

The solution to expand (sec(x)tan(x))(tan(x)-1) is tan^2(x)sec(x)-sec(x)tan(x)

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expand (sec(x)tan(x))(tan(x)-1)

expand

(sec (x) tan (x)) (tan (x) - 1)

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

Solution steps

(sec (x) tan (x)) (tan (x) - 1)

Apply the distributive law:

a (b - c) = ab - a c

(sec (x) tan (x)) (tan (x) - 1) = sec (x) tan (x) tan (x) - sec (x) tan (x) \cdot 1

= sec (x) tan (x) tan (x) - sec (x) tan (x) \cdot 1

Simplify

sec (x) tan (x) tan (x) - sec (x) tan (x) \cdot 1 : tan^{2} (x) sec (x) - sec (x) tan (x)

= tan^{2} (x) sec (x) - sec (x) tan (x)

\frac{( 4 + x ^{2} )}{( 4 - x ^{2} ) ^{2}}

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

\frac{3}{x ( x + 6 )}

\frac{k ^{3} + 5 k ^{2} + 6 k + 4}{2 k ( k + 2 ) ^{2}}

5 (5 + y 15)

What is expand (sec(x)tan(x))(tan(x)-1) ?
The solution to expand (sec(x)tan(x))(tan(x)-1) is tan^2(x)sec(x)-sec(x)tan(x)