Key to "How to simplify 1+tan⁡(x)1+cot⁡(x)?"

Kason Wong

Answered question

2022-12-27

How to simplify

\frac{1 + \tan (x)}{1 + \cot (x)}

Digngoorpr43

Beginner2022-12-28Added 14 answers

\frac{1 + \tan x}{1 + \cot x}

= \frac{1 + \tan x}{1 + \frac{1}{\tan x}}

= \frac{1 + \tan x}{\tan x + 1} \cdot \tan x

Undefined control sequence \cancel

= \tan x

Draven Crane

Beginner2022-12-29Added 1 answers

If you're unsure of where to begin, switch everything to sines and cosines.

\frac{1 + \tan x}{1 + \cot x} = \frac{1 + (\frac{\sin x}{\cos x})}{1 + (\frac{\cos x}{\sin x})}

= \frac{\frac{\cos x + \sin x}{\cos x}}{\frac{\sin x + \cos x}{\sin x}}

= \frac{\frac{1}{\cos x}}{\frac{1}{\sin x}} = \frac{\sin x}{\cos x} = \tan x

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