Question

If `tan θ = 4/3` then (sin θ + cos θ) = ?

Options

• `7/3`

• `7/4`

• `7/5`

• `5/7`

Answer 1

`bb(7/5)`

Explanation:

`tan θ = 4/3`

⇒ `(BC)/(AB) = 4/3`

Let BC = 4k and AB = 3k.

∴ AC² = (AB² + BC²) 

= (9k² + 16k²)

= 25k²

⇒ `AC = sqrt(25k^2)`

⇒ AC = 5k

∴ `(sin θ + cos θ) = ((BC)/(AC) + (AB)/(AC))`

= `((4k)/(5k) + (3k)/(5k))`

= `(7k)/(5k)`

= `7/5`