Final answer to the problem
$\frac{1-\sin\left(a\right)\cos\left(a\right)}{\sin\left(a\right)}$
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Step-by-step Solution
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Factoring by $\tan\left(a\right)$
$\frac{1+\tan\left(a\right)\left(\sin\left(a\right)^2-1\right)}{\sin\left(a\right)}$
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$\frac{1+\tan\left(a\right)\left(\sin\left(a\right)^2-1\right)}{\sin\left(a\right)}$
Learn how to solve problems step by step online. Simplify the trigonometric expression (1+tan(a)sin(a)^2-tan(a))/sin(a). Factoring by \tan\left(a\right). Apply the trigonometric identity: -1+\sin\left(\theta \right)^2=-\cos\left(\theta \right)^2, where x=a. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Multiplying the fraction by \cos\left(a\right)^2.
Final answer to the problem
$\frac{1-\sin\left(a\right)\cos\left(a\right)}{\sin\left(a\right)}$