What is expand (tan(x)+1)^2cos(x) ?

The solution to expand (tan(x)+1)^2cos(x) is tan^2(x)cos(x)+cos(x)+2sin(x)

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expand (tan(x)+1)^2cos(x)

expand

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

tan^{2} (x) cos (x) + cos (x) + 2 sin (x)

Solution steps

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

= cos (x) (tan (x) + 1)^{2}

Expand

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

= cos (x) (tan^{2} (x) + 2 tan (x) + 1)

Apply the distributive law:

m (a + b + c) = ma + mb + m c

cos (x) (tan^{2} (x) + 2 tan (x) + 1) = cos (x) tan^{2} (x) + cos (x) \cdot 2 tan (x) + cos (x) \cdot 1

= cos (x) tan^{2} (x) + cos (x) \cdot 2 tan (x) + cos (x) \cdot 1

Simplify

cos (x) tan^{2} (x) + cos (x) \cdot 2 tan (x) + cos (x) \cdot 1 : tan^{2} (x) cos (x) + cos (x) + 2 sin (x)

= tan^{2} (x) cos (x) + cos (x) + 2 sin (x)

sec (a) csc (a) (tan (a) + cot (a))

(1 + cos (a)) (1 - cos (a))

(x - \frac{1}{x})^{4}

\frac{1}{3} + \frac{2}{9} (0.9 - 1)

\frac{2 ( 2 x ^{2} - x + 3 )}{x}

What is expand (tan(x)+1)^2cos(x) ?
The solution to expand (tan(x)+1)^2cos(x) is tan^2(x)cos(x)+cos(x)+2sin(x)