Prove that: (i) cos 55∘+cos 65∘+cos 175∘=0 (ii) sin 50∘−sin 70∘+sin 10∘=0 (iii) cos 80∘+cos 40∘−cos 20∘=0 (iv) cos 20∘+cos 100∘+cos 140∘=0 (v) sin5π18−cos4π9=√3sinπ9 (vi) cosπ12−sinπ12=1√2 (vii) sin 80∘−cos 70∘=cos 50∘ (viii) sin 51∘−cos 81∘=cos21∘

Prove that: (i) cos 55∘+cos 65∘+cos 175∘=0 (ii) sin 50∘−sin

1.	Prove that: (i) cos 55∘+cos 65∘+cos 175∘=0 (ii) sin 50∘−sin 70∘+sin 10∘=0 (iii) cos 80∘+cos 40∘−cos 20∘=0 (iv) cos 20∘+cos 100∘+cos 140∘=0 (v) sin5π18−cos4π9=√3sinπ9 (vi) cosπ12−sinπ12=1√2 (vii) sin 80∘−cos 70∘=cos 50∘ (viii) sin 51∘−cos 81∘=cos21∘
Answer» Prove that: (i) $c o s 55^{\circ} + c o s 65^{\circ} + c o s 175^{\circ} = 0$ (ii) $s i n 50^{\circ} - s i n 70^{\circ} + s i n 10^{\circ} = 0$ (iii) $c o s 80^{\circ} + c o s 40^{\circ} - c o s 20^{\circ} = 0$ (iv) $c o s 20^{\circ} + c o s 100^{\circ} + c o s 140^{\circ} = 0$ (v) $s i n \frac{5 π}{18} - c o s \frac{4 π}{9} = \sqrt{3} s i n \frac{π}{9}$ (vi) $c o s \frac{π}{12} - s i n \frac{π}{12} = \frac{1}{\sqrt{2}}$ (vii) $s i n 80^{\circ} - c o s 70^{\circ} = c o s 50^{\circ}$ (viii) $s i n 51^{\circ} - c o s 81^{\circ} = c o s 21^{\circ}$