Question

if cota= √3 find the value of cos²a- sin²a/ 2cosa. sina​

Answer 1

Answer:

$\frac{1}{ \sqrt{3} }$

Step-by-step explanation:

$\frac{cos²a- sin²a}{ 2cosa. sina} = \frac{ \cos(2a) }{ \sin(2a) }$

Also,

$\cot(a) = \sqrt{3}$

So,

$a \: = { \cot }^{ - 1} \sqrt{3} = 30$

So, 2a = 2 × 30° = 60°

So,

$\frac{ \cos(2a) }{ \sin(2a) } = \frac{ \cos(60) }{ \sin(60) }$

$= \frac{ \frac{1}{2} }{ \frac{ \sqrt{3} }{2} } = \frac{1}{2} \times \frac{2}{ \sqrt{3} } = \frac{1}{ \sqrt{3} }$