Question

Find the value of θ from the following:

`tan (θ - 15^circ) = 1/sqrt(3)`

Answer 1

Given: `tan (θ - 15^circ) = 1/sqrt(3)`

Step-wise calculation:

1. Recognize the standard value:

`tan 30^circ = 1/sqrt(3)`

So, tan (θ – 15°) = tan 30°

2. Use the identity for equality of tangent:

tan A = tan B

⇒ A = B + n · 180°, n ∈ Z

Hence, θ°15° = 30° + n · 180°

3. Solve for θ:

θ = 45° + n · 180° 

θ = 45° + 180°n (n ∈ Z)

If θ is taken as an acute angle, then θ = 45°.