Question

$\sin {}^{2} ( \alpha ) + \sin {}^{2} (120 + \alpha ) + \sin {}^{2} ( 120 - \alpha )$
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Answer 1

Answer is in attachment


$\sin {}^{2} ( \alpha ) + \sin {}^{2} (120 + \alpha ) + \sin {}^{2} ( 120 - \alpha )$=3/2
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Answer 2

Answer:

3/2

Step-by-step explanation:

sin²α + sin²( 120 + α ) + sin²(120 - α )

⇒ sin²α + sin ( 120 + α )² + sin ( 120 - α )²

⇒ sin²α + ( sin²120 cos²α + cos²120 sin²α + 2 sin 120 cos 120 ) + ( sin²120 cos²α + cos²120 sin²α - 2 sin 120 cos 120

⇒ sin²α + 2 ( sin²120 cos²α + cos²120 sin²α )

⇒ sin²α + 2 ( 3/4 cos²α + 1/4 sin²α )

⇒ sin²α + 3/2 cos²α + 1/2 sin²α

⇒ 3/2 sin²α + 3/2 cos²α

⇒ 3/2 ( sin²α + cos²α )

⇒ 3/2 × 1

⇒ 3/2

$\mathbb{\underline{EXPLANATION}}$

sin ( α + β ) = sin α cos β + cos α sin β .

sin²x + cos²x = 1

The value of sin 120 = √3/2

The value of cos 120 = 1/2