Question

Find the value of the following expression:

cos 90° + cos² 45° sin 30° tan 45°

Answer 1

Given: cos 90° + cos² 45° sin 30° tan 45°

Step-wise calculation:

1. cos 90° = 0.

2. cos 45° = `sqrt(2)/2`

So, `cos^2 45^circ = (sqrt(2)/2)^2`

= `1/2`

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

4. tan 45° = 1.

5. Multiply the factors:

cos² 45° · sin 30° · tan 45° 

= `(1/2) xx (1/2) xx 1`

= `1/4`

6. Add cos 90°:

`0 + 1/4 = 1/4`

The value of the expression is `1/4`.