Here, we show you a step-by-step solved example of trigonometry. This solution was automatically generated by our smart calculator:
Starting from the left-hand side (LHS) of the identity
Combine all terms into a single fraction with $\sec\left(x\right)$ as common denominator
Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}$
Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$
Multiplying fractions $\frac{-\cos\left(x\right)}{\sin\left(x\right)} \times \frac{1}{\cos\left(x\right)}$
Simplify the fraction $\frac{-\cos\left(x\right)}{\sin\left(x\right)\cos\left(x\right)}$ by $\cos\left(x\right)$
The reciprocal sine function is cosecant: $\frac{1}{\sin(x)}=\csc(x)$
Simplify $-\cot\left(x\right)\sec\left(x\right)$ by applying trigonometric identities
Cancel like terms $\csc\left(x\right)$ and $-\csc\left(x\right)$
Applying the trigonometric identity: $\displaystyle\frac{1}{\sec(\theta)}=\cos(\theta)$
Since we have reached the expression of our goal, we have proven the identity
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