Question

Simplifying Trigonometric Expressions-

Simplify the trigonometric expression$\frac{\cot \text{A}-1}{1+\tan (-\text{A})}$

Short answer

On simplifying expression we get $\cot A$

Step-by-step solution

Step 1. Given information.

A trigonometric expression as$\frac{\cot \text{A}-1}{1+\tan (-\text{A})}$

Step 2. Concept used.

Expression must be reduced to its most basic form. Using trigonometric identities, expression can be reduce to basic form.

Step 3. Calculation.

Now, simplify$\frac{\cot \text{A}-1}{1+\tan (-\text{A})}$ using identities:

$$\begin{gathered} \Rightarrow \frac{\cot \text{A}-1}{1-\tan \text{A}}(\because \tan (-A)=-\tan (\text{A}) \\ \Rightarrow \frac{\frac{1}{\tan A}-1}{1-\tan A}\left(\because \cot A=\frac{1}{\tan A}\right) \\ \Rightarrow \frac{1-\tan \text{A}}{(\tan \text{A})(1-\tan \text{A})} \\ \Rightarrow \cot \text{A} \end{gathered}$$