Final answer to the problem
$\frac{\left(\sec\left(a\right)-\tan\left(a\right)\right)\cos\left(a\right)}{\sin\left(a\right)+1}$
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Step-by-step Solution
Learn how to solve factorization problems step by step online. Simplify the trigonometric expression (sec(a)-tan(a))/(sec(a)+tan(a)). Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Combine \sec\left(a\right)+\frac{\sin\left(a\right)}{\cos\left(a\right)} in a single fraction. Applying the trigonometric identity: \cos\left(\theta \right)\sec\left(\theta \right) = 1. Divide fractions \frac{\sec\left(a\right)+\frac{-\sin\left(a\right)}{\cos\left(a\right)}}{\frac{\sin\left(a\right)+1}{\cos\left(a\right)}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}.
Final answer to the problem
$\frac{\left(\sec\left(a\right)-\tan\left(a\right)\right)\cos\left(a\right)}{\sin\left(a\right)+1}$
