Exercise
$\frac{-\cos\left(x\right)}{\sec\left(x\right)+\tan\left(x\right)}$
Step-by-step Solution
Learn how to solve problems step by step online. Simplify the trigonometric expression (-cos(x))/(sec(x)+tan(x)). Rewrite \sec\left(x\right)+\tan\left(x\right) in terms of sine and cosine functions. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Combine fractions with common denominator \cos\left(x\right).
Simplify the trigonometric expression (-cos(x))/(sec(x)+tan(x))
Final answer to the exercise
$\frac{-\cos\left(x\right)^2}{1+\sin\left(x\right)}$