Question

cot 30 cot 60-1 apon cot 30+cot 60= cot 90

Answer 1

heya
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Answer 2

$\dfrac{\cot 30.\cot 60-1}{\cot 30+\cot 60}=\cot 90$, proved.

Step-by-step explanation:

Prove that, $\dfrac{\cot 30.\cot 60-1}{\cot 30+\cot 60}=\cot$90[/tex]

L.H.S. = $\dfrac{\cot 30.\cot 60-1}{\cot 30+\cot 60}$

=$\dfrac{\sqrt{3} \times \frac{1}{\sqrt{3}} -1}{\sqrt{3} +\frac{1}{\sqrt{3}}}$

[ ∵ $\cot 30=\sqrt{3}$ and $\cot 60=\dfrac{1}{\sqrt{3}}$]

$=\dfrac{1 -1}{\frac{3+1}{\sqrt{3}}}$

$=\dfrac{0}{\frac{3+1}{\sqrt{3}}}$

= 0

R.H.S. = $\cot 90$

= 0

[ ∵ $\cot 90=0$]

L.H.S. = R.H.S. = 0, proved.