Question

If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`

Answer 1

We have , 

 5 `tan theta = 4`

⇒ `tan theta = 4/5`

 Now ,

   `((cos theta - sintheta))/(( cos theta + sin theta))`

  `=(((cos theta )/(cos theta)- (sin theta )/(cos theta)))/((cos theta/ cos theta+ sin theta/ cos theta)`                             (𝐷𝑖𝑣𝑖𝑑𝑖𝑛𝑔 𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟 𝑎𝑛𝑑 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 𝑏𝑦 cos θ)

   `=((1- tan theta))/((1+ tan theta))`

   `= ((1/1-4/5))/((1/1+4/5))`

    `= ((1/5))/((9/5))`

    `= 1/9`