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Exercise

$\sin\:\theta\:\cos\:\theta\:\left(\tan\:\theta\:+cot\theta\:\right)$

Step-by-step Solution

1

Simplify $\sin\left(\theta\right)\cos\left(\theta\right)\left(\tan\left(\theta\right)+\cot\left(\theta\right)\right)$ using the trigonometric identity: $\sin(2x)=2\sin(x)\cos(x)$

$\frac{\sin\left(2\theta\right)}{2}\left(\tan\left(\theta\right)+\cot\left(\theta\right)\right)$
2

Multiply the single term $\frac{\sin\left(2\theta\right)}{2}$ by each term of the polynomial $\left(\tan\left(\theta\right)+\cot\left(\theta\right)\right)$

$\tan\left(\theta\right)\frac{\sin\left(2\theta\right)}{2}+\cot\left(\theta\right)\frac{\sin\left(2\theta\right)}{2}$

Final answer to the exercise

$\tan\left(\theta\right)\frac{\sin\left(2\theta\right)}{2}+\cot\left(\theta\right)\frac{\sin\left(2\theta\right)}{2}$

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