Question

If x sin 60° + cos 30° – tan 45° = `sqrt(3)/2`, find the value of x.

Answer 1

Given: x sin 60° + cos 30° – tan 45° = `sqrt(3)/2`

Step-wise calculation:

1. Replace the trig values:

`sin 60^circ = sqrt(3)/2`

`cos 30^circ = sqrt(3)/2` 

tan 45° = 1

So: `x(sqrt(3)/2) + (sqrt(3)/2) - 1 = sqrt(3)/2`.

2. Subtract `sqrt(3)/2` from both sides: 

`x(sqrt(3)/2) + (sqrt(3)/2) - 1 - (sqrt(3)/2) = 0`

⇒ `x(sqrt(3)/2) - 1 = 0`

3. Solve for x:

`x(sqrt(3)/2) = 1`

⇒ `x = 1 ÷ (sqrt(3)/2)`

= `2/sqrt(3)`

4. Rationalize denominator (optional):

`x = 2/sqrt(3) = (2sqrt(3))/3`