(i) cosec 15° = \(\frac{1}{sin\,15°}\)
Consider sin 15° = sin(45° – 30°)
= sin 45° cos 30° – cos 45° sin 30°
cosec 15° = \(\frac{1}{sin\,15°}\) = \(\frac{2\sqrt{2}}{\sqrt{3}-1}\)
(ii) sin (-105°) = -sin (105°) (∵ sin (-θ)
= – sin θ) = -[sin(60° + 45°)]
= -[sin 60° cos 45° + cos 60° sin 45°]
(iii) cot 75° = \(\frac{1}{tan\,75°}\)
Consider tan 75° = tan (30° + 45°)
cot 75° = \(\frac{1}{tan\,75°}\) = \(\frac{\sqrt{3}-1}{\sqrt{3}+1}\)
