Answer:
in steps
Step-by-step explanation:
cos 15° = cos (45° - 30°) = cos 45° cos 30° + sin 45° sin 30°
= (√2 / 2) (√3 / 2) + (√2 / 2) (1 / 2)
= (√3/2√2) + (1/2√2)
= (√3 + 1) / 2√2 (0.9659)
cot 165° = cot (90° + 75°) = - tan 75° = - (2 + √3)
csc 15° = 1 / sin 15° = 1 / sin (45° - 30°)
= 1 / (sin 45° cos 30° - cos 45° sin 30°)
= 1 / ( √2/2 x √3/2 - √2/2 x 1/2)
= 1 / ((√6 - √2) / 4)
= 4 / (√6 - √2)
=√6 + √2
