# Evaluate: cos(θ)^2 * ((sin(θ))/(cos(θ)) * tan(θ)+1)

## Expression: ${\cos\left({θ}\right)}^{2} \times \left( \frac{ \sin\left({θ}\right) }{ \cos\left({θ}\right) } \times \tan\left({θ}\right)+1 \right)$

Use $\frac{ \sin\left({t}\right) }{ \cos\left({t}\right) }=\tan\left({t}\right)$ to transform the expression

${\cos\left({θ}\right)}^{2} \times \left( \tan\left({θ}\right)\tan\left({θ}\right)+1 \right)$

The factor $\tan\left({θ}\right)$ repeats $2$ times, so the base is $\tan\left({θ}\right)$ and the exponent is $2$

${\cos\left({θ}\right)}^{2} \times \left( {\tan\left({θ}\right)}^{2}+1 \right)$

Use $\tan\left({t}\right)=\frac{ \sin\left({t}\right) }{ \cos\left({t}\right) }$ to transform the expression

${\cos\left({θ}\right)}^{2} \times \left( {\left( \frac{ \sin\left({θ}\right) }{ \cos\left({θ}\right) } \right)}^{2}+1 \right)$

To raise a fraction to a power, raise the numerator and denominator to that power

${\cos\left({θ}\right)}^{2} \times \left( \frac{ {\sin\left({θ}\right)}^{2} }{ {\cos\left({θ}\right)}^{2} }+1 \right)$

Write all numerators above the common denominator

${\cos\left({θ}\right)}^{2} \times \frac{ {\sin\left({θ}\right)}^{2}+{\cos\left({θ}\right)}^{2} }{ {\cos\left({θ}\right)}^{2} }$

Use ${\sin\left({t}\right)}^{2}+{\cos\left({t}\right)}^{2}=1$ to simplify the expression

${\cos\left({θ}\right)}^{2} \times \frac{ 1 }{ {\cos\left({θ}\right)}^{2} }$

Cancel out the common factor ${\cos\left({θ}\right)}^{2}$

$1$

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