Question

In the following questions, two statements (i) and (ii) are given. Choose the valid statement.

(i) If `tan θ = 3/4`, then `cos θ = 3/5`

(ii) If sin θ = 3 cos θ, then `(sin θ - cos θ)/(sin θ + cos θ) = 1/2`

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (ii)

Explanation:

(i) False. `tan θ = "Opposite"/"Adjacent"`

= `3/4` 

So, the triangle sides are 3, 4, 5.

Therefore, `cos θ = "Adjacent"/"Hypotenuse"`

= `4/5`, not `3/5`

(ii) True. If sin θ = 3 cos θ, write sin θ = 3c and cos θ = c (c ≠ 0).

Then `(sin θ - cos θ)/(sin θ + cos θ)`

= `(3c - c)/(3c + c)`

= `(2c)/(4c)`   ...(Sign of c cancels)

= `1/2`