Question

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

(i) In ΔАВС, ∠A = 90° and sin B = `8/17` then cos B = `15/17`.

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

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (i)

Explanation:

(i) In a right triangle with A = 90°, B is acute.

So, `cos B = +sqrt(1 - sin^2B)`

= `sqrt(1 - (8/17)^2)`

= `sqrt(225/289)`

= `15/17`

(ii) If `sin θ = 1/3` then `cos θ = ±sqrt(1 - (1/3)^2)`

= `±sqrt(8/9)`

= `±(2sqrt(2))/3`, which is not `2/3`. 

So, (ii) is false.