tan 37,5derajat+tan82,5derajat

Trigonometri.

tan A + tan B = sin A / cos A + sin B / cos B
= (sin A cos B + cos A sin B) / (cos A cos B)
= 2 sin (A + B) / [cos (A + B) + cos (A - B)]
Dan ingat, cos (-θ) = cos θ

tan 37,5° + tan 82,5°
= 2 sin (37,5° + 82,5°) / [cos (37,5° + 82,5°) + cos (37,5° - 82,5°)]
= 2 sin 120° / (cos 120° + cos 45°)
= 2 (1/2 √3) / (-1/2 + 1/2 √2)
= √3 / (√2 - 1) / 2
= 2√3 / (√2 - 1) [(√2 + 1) / (√2 + 1)]
= 2(√6 + √3)