Trigonometry Examples

$\cot^{2} (0) + \csc^{2} (0) = 1$

Step 1

Simplify the left side.

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Step 1.1

Simplify ${(\frac{\cos (0)}{0})}^{2} + \csc^{2} (0)$ .

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Step 1.1.1

Rewrite $\csc (0)$ in terms of sines and cosines.

${(\frac{\cos (0)}{0})}^{2} + {(\frac{1}{\sin (0)})}^{2} = 1$

Step 1.1.2

The exact value of $\sin (0)$ is $0$ .

${(\frac{\cos (0)}{0})}^{2} + {(\frac{1}{0})}^{2} = 1$

Step 1.2

The equation cannot be solved because it is undefined.

$Undefined$

Step 2

The left side has no solution, which means that the given statement is false.

False