Question

If 5 ${\displaystyle \tan \theta =4,\text{write the value of}\frac{(\cos \theta -\sin \theta )}{(\cos \theta +\sin \theta )}}$

Answer 1

We have , 

 5 ${\displaystyle \tan \theta =4}$

⇒ ${\displaystyle \tan \theta =\frac{4}{5}}$

 Now ,

   ${\displaystyle \frac{(\cos \theta -\sin \theta )}{(\cos \theta +\sin \theta )}}$

  ${\displaystyle =\frac{(\frac{\cos \theta }{\cos \theta }-\frac{\sin \theta }{\cos \theta })}{(\frac{\cos \theta }{\cos \theta }+\frac{\sin \theta }{\cos \theta })}}$                             (𝐷𝑖𝑣𝑖𝑑𝑖𝑛𝑔 𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟 𝑎𝑛𝑑 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 𝑏𝑦 cos θ)

   ${\displaystyle =\frac{(1-\tan \theta )}{(1+\tan \theta )}}$

   ${\displaystyle =\frac{(\frac{1}{1}-\frac{4}{5})}{(\frac{1}{1}+\frac{4}{5})}}$

    ${\displaystyle =\frac{\left(\frac{1}{5}\right)}{\left(\frac{9}{5}\right)}}$

    ${\displaystyle =\frac{1}{9}}$