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Proving trigonometric identities Calculator

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1

Solved example of proving trigonometric identities

$\cot\left(x\right)\cdot\sec\left(x\right)=\csc\left(x\right)$
2

Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$

$\cot\left(x\right)\frac{1}{\cos\left(x\right)}=\csc\left(x\right)$
3

Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$

$\cot\left(x\right)\frac{1}{\cos\left(x\right)}=\frac{1}{\sin\left(x\right)}$
4

Apply the formula: $\cot\left(x\right)$$=\frac{\cos\left(x\right)}{\sin\left(x\right)}$

$\frac{\cos\left(x\right)}{\sin\left(x\right)}\cdot\frac{1}{\cos\left(x\right)}=\frac{1}{\sin\left(x\right)}$
5

Multiplying fractions

$\frac{\cos\left(x\right)}{\sin\left(x\right)\cos\left(x\right)}=\frac{1}{\sin\left(x\right)}$
6

Simplify the fraction by $\cos\left(x\right)$

$\frac{1}{\sin\left(x\right)}=\frac{1}{\sin\left(x\right)}$
7

Both expressions are equal

true

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