Practicing Success
If $cot75° = 2 - \sqrt{3}.$ Find the value of cot 15°. |
$2-\sqrt{3}$ $2+\sqrt{3}$ $\sqrt{3}+1$ $\sqrt{3}-1$ |
$2+\sqrt{3}$ |
cot 75º = 2 - √3 We know, tanA = cotB Iff A + B = 90º So, cot 75º = tan 15º Now, cot 15º = \(\frac{1}{tan15º}\) = \(\frac{1}{ 2 - √3 }\) Multiply and divide by ( 2 + √3 ) = \(\frac{1}{ 2 - √3 }\) × \(\frac{ 2+ √3 }{ 2+ √3 }\) = \(\frac{ 2+ √3 }{ 4-3 }\) = 2+ √3 |