Question

Find the value of the following expression:

2 sin² 30° – 3 cos² 45° + tan² 60°

Answer 1

Given: 2 sin² 30° – 3 cos² 45° + tan² 60°

Step-wise calculation:

`sin 30^circ = 1/2`

⇒ `sin^2 30^circ = (1/2)^2`

= `1/4`

⇒ `2 xx (1/4) = 1/2`

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

⇒ `cos^2 45^circ = (sqrt(2)/2)^2`

= `1/2`

⇒ `-3 xx (1/2) = -3/2`

`tan 60^circ = sqrt(3)`

⇒ `tan^2 60^circ = (sqrt(3))^2`

= 3

Now sum: `1/2 - 3/2 + 3`

= `(1/2 - 3/2) + 3` 

= –1 + 3

= 2

The value of the expression is 2.