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
Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}$
Multiplying the fraction by $\cos\left(x\right)$
When multiplying two powers that have the same base ($\cos\left(x\right)$), you can add the exponents
Multiplying the fraction by $\cos\left(x\right)$
Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$
The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors
Combine and simplify all terms in the same fraction with common denominator $\sin\left(x\right)$
Apply the trigonometric identity: $1-\cos\left(\theta \right)^2$$=\sin\left(\theta \right)^2$
Simplify the fraction $\frac{\sin\left(x\right)^2}{\sin\left(x\right)}$ by $\sin\left(x\right)$
Since we have reached the expression of our goal, we have proven the identity
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