Question

find the value of :-
cot30° - cot75° / tan15° - tan60°

Answer 1

(cot30 - cot75)/(tan15 - tan60) 
= [tan(90-30) - tan(90-75)]/(tan15 - tan60) { since cotA = tan(90-A)} 
= [tan60 - tan15)/-{tan15 - tan60} 
= -1

Answer 2

$\frac{\cot 30^\circ-\cot 75^\circ}{\tan15^\circ-\tan 60^\circ=-1$

Step-by-step explanation:

Given : Expression $\frac{\cot 30^\circ-\cot 75^\circ}{\tan15^\circ-\tan 60^\circ}$

To find : The value of expression ?

Solution :

$\frac{\cot 30^\circ-\cot 75^\circ}{\tan15^\circ-\tan 60^\circ}$

Re-write the numerator as, $\tan(90-\theta)=\cot\theta$

$=\frac{\tan(90-30)^\circ - \tan(90-75)^\circ}{\tan15^\circ-\tan 60^\circ}$

$=\frac{\tan(60)^\circ - \tan(15)^\circ}{\tan15^\circ-\tan 60^\circ}$

$=-\frac{\tan15^\circ-\tan 60^\circ}{\tan15^\circ-\tan 60^\circ}$

$=-1$

Therefore, $\frac{\cot 30^\circ-\cot 75^\circ}{\tan15^\circ-\tan 60^\circ=-1$

#Learn more

Tan(A) + tan(60+A) + tan(60-A) =

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