Question

Without using trigonometric tables find the value of 3 sin² 45° + 2 cos² 60°.

Answer 1

Given: 3 sin² 45° + 2 cos² 60°

Step-wise calculation:

1. `sin 45^circ = sqrt(2)/2` and `cos 60^circ = 1/2`.

2. `sin^2 45^circ = (sqrt(2)/2)^2`

= `1/2`

3. `cos^2 60^circ = (1/2)^2`

= `1/4`

4. `3 xx (1/2) + 2 xx (1/4)`

= `3/2 + 1/2` 

= 2