What is expand 2sec^5(x)sin(x)(1+sin^2(x)) ?

The solution to expand 2sec^5(x)sin(x)(1+sin^2(x)) is (2sin^3(x)+2sin(x))/(cos^5(x))

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expand 2sec^5(x)sin(x)(1+sin^2(x))

expand

2 sec^{5} (x) sin (x) (1 + sin^{2} (x))

\frac{2 sin ^{3} ( x ) + 2 sin ( x )}{cos ^{5} ( x )}

Solution steps

2 sec^{5} (x) sin (x) (1 + sin^{2} (x))

Apply the distributive law:

a (b + c) = ab + a c

2 sec^{5} (x) sin (x) (1 + sin^{2} (x)) = 2 sec^{5} (x) sin (x) \cdot 1 + 2 sec^{5} (x) sin (x) sin^{2} (x)

= 2 sec^{5} (x) sin (x) \cdot 1 + 2 sec^{5} (x) sin (x) sin^{2} (x)

Simplify

2 sec^{5} (x) sin (x) \cdot 1 + 2 sec^{5} (x) sin (x) sin^{2} (x) : \frac{2 sin ^{3} ( x ) + 2 sin ( x )}{cos ^{5} ( x )}

= \frac{2 sin ^{3} ( x ) + 2 sin ( x )}{cos ^{5} ( x )}

(k + 1) (\frac{1}{2} + \frac{1}{4})

(x - 7) (x + 2 + 3)

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

12 x^{12 x} (ln (x) + 1) \cdot (sin^{6 x} (x))

(\frac{3 a}{5} + \frac{b}{2}) (\frac{3 a}{5} - \frac{b}{2})

What is expand 2sec^5(x)sin(x)(1+sin^2(x)) ?
The solution to expand 2sec^5(x)sin(x)(1+sin^2(x)) is (2sin^3(x)+2sin(x))/(cos^5(x))