Question

Prove that:
cot 90°
)
cot 30° cot 60° - 1
cot 30° + cot 60°​

Answer 1

Answer:

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

cot30+cot60

cot30.cot60−1

=cot90 , proved.

Step-by-step explanation:

Prove that, \dfrac{\cot 30.\cot 60-1}{\cot 30+\cot 60}=\cot

cot30+cot60

cot30.cot60−1

=cot 90[/tex]

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

cot30+cot60

cot30.cot60−1

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

3

+

3

1

3

×

3

1

−1

[ ∵ \cot 30=\sqrt{3}cot30=

3

and \cot 60=\dfrac{1}{\sqrt{3}}cot60=

3

1

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

3

3+1

1−1

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

3

3+1

0

= 0

R.H.S. = \cot 90cot90

= 0

[ ∵ \cot 90=0cot90=0

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

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

ans of the question of math