Question

If Tanø =a/b Find the value of sinø+cosø/sinø-cosø

Answer 1

`(b+a)/(b-a)`

Explanation:

Tan θ =
`(perpendicular)/(base)` =
`(b)/(a)`

So, Perpendicular = b, base = a

Finding hypotenuse by Pythagorean Theorem:

`c^2 = a^2+b^2`

=> So, hypotenuse = c

Sin θ =
`(perpendicular)/(hypotenuse)= (b)/(c)`

Cos θ =
`(base)/(hypotenuse)= (a)/(c)`

So, Now finding
`(sin\theta+cos\theta)/(sin\theta-cos\theta)`

=>
`(b)/(c) + (a)/(c)` ÷
`(b)/(c) - (a)/(c)`

=>
`(b+a)/(c)` ÷
`(b-a)/(c)`

=>
`(b+a)/(c) * (c)/(b-a)`

=>
`(b+a)/(b-a)`