Question

Find the value of:

`sqrt((1-sin^2 30°)/(1- cos^2 30°))`

Answer 1

Given:

Step 1:

1 − sin² θ = cos² θ

1 − cos² θ = sin² θ

`sqrt (cos^2 30°)/sin^2 30°`

Step 2: Remove the square

= `(cos 30°)/(sin 30°)`

Step 3: Substitute values

cos 30° = `sqrt3/2`

sin 30° = `1/2`

= `((sqrt3)/2)/(1/2) = sqrt3`