Question

The value of (sin 30° + cos 30°)² – (sin 60° – cos 60)² is ______.

Answer 1

The value of (sin 30° + cos 30°)² – (sin 60° – cos 60)² is `underlinebb(sqrt(3))`.

Explanation:

Let `sin 30^circ = 1/2, cos 30^circ = sqrt(3)/2`

`sin 60^circ = sqrt(3)/2, cos 60^circ = 1/2` 

Then `(sin 30^circ + cos 30^circ)^2 = ((1 + sqrt(3))/2)^2 = 1 + sqrt(3)/2` 

`(sin 60^circ - cos 60^circ)^2 = ((sqrt(3) - 1)/2)^2 = 1 - sqrt(3)/2` 

Subtracting gives `(1 + sqrt(3)/2) - (1 - sqrt(3)/2) = sqrt(3)`