Without using trigonometric tables, evaluate:
(i)cos 48∘−sin 42∘
(ii)cosec 31∘−sec 59∘
(iii)cot 34∘−tan 56∘
(iv)cos2 13∘−sin2 77∘ [4 MARKS]
Solution: 1 Mark each
(i)cos 48∘−sin 42∘=cos(90∘−42∘)−sin 42∘
=sin 42∘−sin 42∘=0
[∵cos(90∘−θ)=sin θ]
(ii)cosec 31∘−sec 59∘=cosec(90∘−59∘)−sec 59∘
=sec 59∘−sec 59∘=0
[∵cosec(90∘−θ)=sec θ]
(iii)cot 34∘−tan 56∘=cot(90∘−56∘)−tan 56∘
=tan 56∘−tan 56∘=0
[∵cot(90∘−θ)=tan θ]
(iv)cos2 13∘−sin2 77∘=cos2 (90∘−77∘)−sin2 77∘
=sin2 77∘−sin2 77∘=0
[∵cos(90∘−θ)=sin θ]