Trigonometry Examples

$\csc (π) - \cot (π) = 1$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{1}{0} - \cot (π)$ .

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Step 1.1.1

Rewrite $\cot (π)$ in terms of sines and cosines.

$\frac{1}{0} - \frac{\cos (π)}{\sin (π)} = 1$

Step 1.1.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\frac{1}{0} - \frac{\cos (π)}{\sin (0)} = 1$

Step 1.1.3

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

$\frac{1}{0} - \frac{\cos (π)}{0} = 1$

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