Question

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

(i) sin 60° · cos 60° = `sqrt(3)/2`

(ii) sin x = cos x then x = 45°

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (ii)

Explanation:

(i) sin 60° · cos 60° = `sqrt(3)/2 · 1/2` 

= `sqrt(3/4)`, not `sqrt(3/2)`

So, (i) is false.

(ii) sin x = cos x

⇒ tan x = 1 

So, x = 45° more generally x = 45° + k · 180° and if x is taken as an acute angle, then x = 45°. 

Hence, (ii) is true.