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Sin12°.sin48°.sin54°.answer it quickly​

Answer»

ANSWER

FORMULA USED

1. sinx.sin(60-x) sin(60+x) = 1/4 sin(3x)

2. sin(90-x) = cos x

3. sin2x = 2sinxcosx

SOLUTION

sin12. sin48. sin54

=> sin12. sin48. sin54. SIN72/sin72

=> USE formula SINCE x = 12

=> sin36 . sin54/ 4 × sin72

=> now sin72 = cos 18

and sin36 = 2cos18.sin18

=> we get finally after cancelling terms

=> sin18. sin54 / 2

=> some direct values of function

sin18 = √5-1/4 sin54 = √5+1/4

=> (√5-1 / 4)(√5+1 / 4) / 2

=> ( 5 -1 ) / 16

2

=> 4

16 ×2

=> 1/8

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