Question

Find the value of the following expression:

4 cos² 60° + 4 sin² 45° – sin² 30°

Answer 1

Given: 4 cos² 60° + 4 sin² 45° – sin² 30°

Step-wise calculation:

1. `cos 60^circ = 1/2` 

So, `cos^2 60° = (1/2)^2` 

= `1/4` 

⇒ `4 xx cos^2 60^circ = 4 xx (1/4)` 

= 1

2. `sin 45^circ = sqrt(2)/2` 

So, `sin^2 45^circ = (sqrt(2)/2)^2` 

= `1/2` 

⇒ `4 xx sin^2 45^circ = 4 xx (1/2)` 

= 2

3. `sin 30^circ = 1/2`

So, `sin^2 30^circ = (1/2)^2`

= `1/4`

Combine: `1 + 2 - 1/4` 

= `3 - 1/4` 

= `11/4`

The value of the expression is `11/4`, which is 2.75.