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Starting from the left-hand side (LHS) of the identity
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$\frac{1+\csc\left(x\right)}{\cot\left(x\right)+\cos\left(x\right)}$
Learn how to solve problems step by step online. Prove the trigonometric identity (1+csc(x))/(cot(x)+cos(x))=sec(x). Starting from the left-hand side (LHS) of the identity. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Combine all terms into a single fraction with \sin\left(x\right) as common denominator. Divide fractions \frac{1+\csc\left(x\right)}{\frac{\cos\left(x\right)+\cos\left(x\right)\sin\left(x\right)}{\sin\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}.