Question

If tan a=3/5 find sin a+cos a/sin a-cos a

Answer 1

Step-by-step explanation:

There are two ways to solve this:

#1. The value of tan a = 3/5. That means

your perpendicular and base ratio in a right angled triangle is given. From this you can calculate the hypotenuse using pythagoras theorem. And hence you can get (sin a) and (cos a). Substitute it and solve, you will get the answer. Trust me this is a good way.

But i opt for a slightly different procedure.

#2. Dividing numerator and denominator by

cos (a) :

{(sin a/cos a) + (cos a/cos a)} / {(sin a/cos a) - (cos a/cos a)}

This looks complicated but it is not. You just have to divide everything by (cos a).

now,

(sin a/cos a) = tan a

(cos a/cos a) = 1.

So our equation become:

(tan a + 1) / (tan a - 1)

now we know tan a = 3/5. Substitute it :

(3/5 + 1) / (3/5 - 1)

= (8/5) / (-2/5)

= -4

This process reduces calculation. Thats all

Both process are equally good based on yours convienence. If any query feel free to ask.