Prove that: (i)tan720∘−cos270∘−sin150∘cos120∘=14 (ii)sin78

1.	Prove that: (i)tan720∘−cos270∘−sin150∘cos120∘=14 (ii)sin780∘sin480∘+cos120∘sin150∘=12 (iii)sin780∘sin120∘+cos240∘sin390∘=12 (iv)sin600∘cos390∘+cos480∘sin150∘=−1 (v)tan250∘cot405∘+tan765∘cot675∘=0
Answer» Prove that: $(i) t a n 720^{\circ} - c o s 270^{\circ} - s i n 150^{\circ} c o s 120^{\circ} = \frac{1}{4}$ $(i i) s i n 780^{\circ} s i n 480^{\circ} + c o s 120^{\circ} s i n 150^{\circ} = \frac{1}{2}$ $(i i i) s i n 780^{\circ} s i n 120^{\circ} + c o s 240^{\circ} s i n 390^{\circ} = \frac{1}{2}$ $(i v) s i n 600^{\circ} c o s 390^{\circ} + c o s 480^{\circ} s i n 150^{\circ} = - 1$ $(v) t a n 250^{\circ} c o t 405^{\circ} + t a n 765^{\circ} c o t 675^{\circ} = 0$

Prove that: (i)tan720∘−cos270∘−sin150∘cos120∘=14 (ii)sin780∘sin480∘+cos120∘sin150∘=12 (iii)sin780∘sin120∘+cos240∘sin390∘=12 (iv)sin600∘cos390∘+cos480∘sin150∘=−1 (v)tan250∘cot405∘+tan765∘cot675∘=0

Answer»

Prove that:

$(i) t a n 720^{\circ} - c o s 270^{\circ} - s i n 150^{\circ} c o s 120^{\circ} = \frac{1}{4}$

$(i i) s i n 780^{\circ} s i n 480^{\circ} + c o s 120^{\circ} s i n 150^{\circ} = \frac{1}{2}$

$(i i i) s i n 780^{\circ} s i n 120^{\circ} + c o s 240^{\circ} s i n 390^{\circ} = \frac{1}{2}$

$(i v) s i n 600^{\circ} c o s 390^{\circ} + c o s 480^{\circ} s i n 150^{\circ} = - 1$

$(v) t a n 250^{\circ} c o t 405^{\circ} + t a n 765^{\circ} c o t 675^{\circ} = 0$