Question

Find the value of _tan 38 - cot 22

Answer 1

Thank you for asking this question.

Here is your answer.

tan 38° - cot 22°

= sin 38°/cos 38° - cos 22°/sin 22°

= sin 38° sin 22° - cos 38° cos 22°/ cos 38° sin 22°/ cos 38° sin 22°

= - cos (38° + 22°)/ cos 38° sin 22°

= - cos 60° / cos 38° sin 22°

= -1 sec 38°/2 cos sec 22°

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Answer 2

The value of $\tan 38 - \cot 22$ is -$\dfrac{1}{\cos (106) -\cos (30)}.$

Step-by-step explanation:

We have,

$\tan 38 - \cot 22$

$= [tex]\tan 38 - \cot (90-68)$

$=\tan 38 - \tan 68$

[ ∵ $\cot (90-\theta)= \tan \theta$ ]

$= \dfrac{\sin 38}{\cos 38} - \dfrac{\sin 68}{\cos 68}$

$=\dfrac{\sin 38\times \cos 68-\cos 38\times \sin 68}{\cos 68\times \cos 38}$

$=2\dfrac{\sin (38-68)}{2\cos 68\times \cos 38}$

$=2\dfrac{\sin (-30)}{\cos (68 + 38) -\cos (68 - 38)}$

$=-2\dfrac{\frac{1}{2}}{\cos (106) -\cos (30)}$

$=-\dfrac{1}{\cos (106) -\cos (30)}$

Hence, the value of $\tan 38 - \cot 22$ is -$\dfrac{1}{\cos (106) -\cos (30)}.$