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ABC is a right triangle right-angled at C and AC=√3 BC. Prove that ∠ABC=60o.
Ans: Tan B = AC/BC
Tan B = √3 BC/BC
Tan B =√3
⇒ Tan B = Tan 60
⇒ B = 60o
⇒ ∠ABC = 60o
Hence proved
sin10+sin20+sin30+....+sin360=0 sin10+sin20+sin30+sin40+...sin180+sin(360-170)+......+sin(360-40)+sin(360-30)+sin(360-20)+sin360-10)+sin360 sin360-x=-sinx hence all terms cancel
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