Question

Find each exact value. Use a sum or difference identity. tan 75°

Answer 1

Explanation:

We know that,

tan(a + b) = (tan a + tan b)/(1 - tan a tan b)

Let a = 30° and b = 45°

tan(75°) = tan(30° + 45°) = (tan 30° + tan 45°)/(1 - tan 30° tan 45°)

= (1/√3 + 1)/(1 - (1/√3) * 1)

= (√3 + √3)/(√3 - 1)

= 2√3 / (√3 - 1)

= (2√3 * (√3 + 1))/((√3 - 1) * (√3 + 1))

= (2√3 * √3 + 2√3 * 1)/(3 - 1)

= (6√3 + 2)/(2)

= 3 + √3