Question

Find the value of the following expression:

`(sin^2 45^circ + cos^2 45^circ)/(tan^2 60^circ)`

Answer 1

Given: `(sin^2 45^circ + cos^2 45^circ)/(tan^2 60^circ)`

Step-wise calculation:

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

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

= `1/2 + 1/2`

= 1

3. `tan 60^circ = sqrt(3)`.

So, `tan^2 60^circ = (sqrt(3))^2 = 3`.

4. Therefore, the expression = `1/3`.