Question

cosa -sina/cosa+sina=1-√3/1+√3​

Answer 1

cosa-sina/cosa+sina=1-√3/1+√3

By componendo and dividendo rule

cosa-sina+cosa+sina/cosa-sina-(cosa+sina) =1-√3+1+√3/1-√3-(1+√3)

by simplification we get cota=1/√3

a

so a=60degrees

Answer 2

The value of sina is and cos a is

Given:

A equation $\frac{cosa-sina}{cosa+sina}=\frac{1-\sqrt{3} }{1+\sqrt{3} }$

To Find:

The value of sina and cosa

Solution:

The equation is $\frac{cosa-sina}{cosa+sina}=\frac{1-\sqrt{3} }{1+\sqrt{3} }$

Apply componendo and dividendo rule here

$\frac{cosa-sina+cosa+sina}{cosa-sina-cosa-sina}= \frac{1-\sqrt{3}+1+\sqrt{3} }{1-\sqrt{3}-1-\sqrt{3} } \\\frac{2cos}{-2sina}=\frac{2}{-2\sqrt{3} } \\\frac{cosa}{sina}=\frac{1}{\sqrt{3} }$

By comparing we get cosa = 1 and sina is √3.

Hence, the value of sina is √3 and cosa is 1.

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