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