Question

Prove (cos11+sin11)/(cos 11 - sin 11)=tan 56

Answer 1

Notice that 56° = 45° + 11°. Then

tan(56°) = sin(56°) / cos(56°)

… = sin(45° + 11°) / cos(45° + 11°)

… = (sin(45°) cos(11°) + cos(45°) sin(11°)) / (cos(45°) cos(11°) - sin(45°) sin(11°))

Recall that sin(45°) = cos(45°) = 1/√2, so we can cancel each term involving 45° :

tan(56°) = (cos(11°) + sin(11°)) / (cos(11°) - sin(11°))