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Select the correct answer from the drop-down menu. Simplify the expression. (1-cot(r))^2/cot(r)

Sagot :

The simplified form of the given expression is tan(r) + cot(r) - 2

Simplifying trigonometric functions

From the question, we are to simplify the given trigonometric function

The given trigonometric function is

[tex]\frac{(1-cot(r))^{2} }{cot(r)}[/tex]

Expanding, we get

[tex]\frac{(1-cot(r))(1-cot(r)) }{cot(r)}[/tex]

Simplifying

[tex]\frac{1 - 2cot(r) +cot^{2}(r) }{cot(r)}[/tex]

[tex]\frac{1}{cot(r)} -\frac{2cot(r)}{cot(r)}+\frac{cot^{2}(r) }{cot(r)}[/tex]

[tex]\frac{1}{cot(r)} -2+cot(r)[/tex]

Recall: [tex]tan(x) = \frac{1}{cot(x)}[/tex]

Therefore, we get

[tex]tan(r) -2 + cot(r)[/tex]

[tex]tan(r) + cot(r)-2[/tex]

Hence, the simplified form of the given expression is tan(r) + cot(r) - 2.

Learn more on Simplifying Trigonometric functions here: https://brainly.com/question/15538894

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