Question

Find the value of the following expression:

`(sin 30^circ -  sin 90^circ +  2  cos 0^circ)/(tan 30^circ xx tan 60^circ)`

Answer 1

Given: `(sin 30^circ -  sin 90^circ +  2  cos 0^circ)/(tan 30^circ xx tan 60^circ)`

Step-wise calculation:

1. Evaluate basic trig values:

`sin 30^circ = 1/2` 

sin 90° = 1

cos 0° = 1

`tan 30^circ = 1/sqrt(3)` 

`tan 60^circ = sqrt(3)`

2. Substitute into the expression:

Numerator = `1/2 - 1 + 2 xx 1` 

= `1/2 - 1 + 2`

= `3/2` 

Denominator = `1/sqrt(3) xx sqrt(3)`

= 1

3. Value = `(3/2)/1` 

= `3/2`

= 1.5

The value of the expression is `3/2` (1.5).