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