Question

sin20°+sin40°-sin80°
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Answer 1

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Answer 2

Answer:

0

Step-by-step explanation:

Recall sin(A+B) = sin A cos B + cos A sin B

So

  sin 80° = sin( 60° + 20° ) = sin 60° cos 20° + sin 20° cos 60°

and

  sin 40° = sin( 60° - 20° ) = sin 60° cos 20° - sin 20° cos 60°

Putting these into the given expression gives

   sin20°+sin40°-sin80°

= sin 20° + sin 60° cos 20° - sin 20° cos 60° - sin 60° cos 20° - sin 20° cos 60°

= sin 20° - 2 sin 20° cos 60°

= sin 20° - sin 20°        [ since cos 60° = 1/2 ]

= 0

Hope this helps!