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Applying the trigonometric identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$
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$\sec\left(x\right)+\frac{-\cos\left(x\right)}{1+\sin\left(x\right)}$
Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression 1/cos(x)+(-cos(x))/(1+sin(x)). Applying the trigonometric identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Apply the trigonometric identity: \sin\left(\theta \right)=\frac{\sqrt{\sec\left(\theta \right)^2-1}}{\sec\left(\theta \right)}. Combine all terms into a single fraction with \sec\left(x\right) as common denominator. Divide fractions \frac{-\cos\left(x\right)}{\frac{\sec\left(x\right)+\sqrt{\sec\left(x\right)^2-1}}{\sec\left(x\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}.