Question

Use the formula, `cos θ = sqrt((1 + cos 2θ)/2`, find the value of cos 30°, it being given that cos 60° = `1/2`.

Answer 1

Given: `cos θ = sqrt((1 + cos 2θ)/2` and cos 60° = `1/2`.

Step-wise calculation:

1. Let θ = 30°, so 2θ = 60°.

2. Substitute:

`cos 30^circ = sqrt((1 + cos 60^circ)/2)`

3. Using cos 60° = `1/2`:

`cos 30^circ = sqrt((1 + 1/2)/2)`

= `sqrt((3/2)/2)`

= `sqrt(3/4)`

= `sqrt(3)/2`

4. 30° lies in the first quadrant, so cosine is positive.

`cos 30^circ = sqrt(3)/2`.