Question

Answer this✑

✑ Don't answer if ya don't know.
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Answer 1

Answer:

- 3 /4

Step-by-step explanation:

sin ( 2π/3 + a ) = sin ( π - ( π/3 - a ) ⇒ sin ( π/3 - a )

sin ( 4π/3 + a ) = sin ( π +( π/3 +a ) ⇒ -sin ( π/3 + a )

sin a

if we add all 3 equations

we will get sin 60 cos a - cos 60 sin a - [ sin 60 cos a + cos 60 sin a ]+sin a

= -  2 cos 60 sin a + sin a = 0

so we know if a+b+c = 0

a³+b³+c³ =3 abc

so ⇒- 3 sin a sin(60-a) sin(60+a) * 1 / 3 sin a - 4 sin³a

⇒ -3[ sin²60 cos²a - cos²60 sin²a ] * 1 /3 - 4 sin²a

⇒-3[ 3 cos²a - sin²a /4 ]  * 1 /3 - 4 sin²a

⇒ -3 [ 3 - 4 sin²a /4 ]  * 1 /3 - 4 sin²a

= - 3/4