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Starting from the left-hand side (LHS) of the identity
Divide fractions $\frac{\sin\left(x\right)}{\frac{1}{\sin\left(x\right)}}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$
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$\frac{\sin\left(x\right)}{\frac{1}{\sin\left(x\right)}}+\frac{\cos\left(x\right)}{\frac{1}{\cos\left(x\right)}}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity sin(x)/(1/sin(x))+cos(x)/(1/cos(x))=1. Starting from the left-hand side (LHS) of the identity. Divide fractions \frac{\sin\left(x\right)}{\frac{1}{\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}. Divide fractions \frac{\cos\left(x\right)}{\frac{1}{\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}. Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1.