Question

sin12°.sin48°.sin54°.
answer it quickly
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Answer 1

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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Answer 2

Step-by-step explanation:

Let the expression be 'x'

x=sin(12)sin(48)sin(54)

[sin(12)sin(48)]sin(54)

sin(54)*[cos(48-12)- cos(48+12)]/2

sin(54)*[cos(36)- cos(60)]/2

sin(54)*[cos(36)- 1/2] /2

cos(36)* [cos(36)/2-1/4]

cos sq.(36)/2- cos(36)/4

cos(36)= (1+√5)/4

x sq.= cos sq. (36)/2- cos(36)/4

[(1+√5)/4] sq/2-[(1+√5/4)]/4

(1+√5)sq/32-(1-√5)/16

(6+2√5)/32-(1+√5)/16

(6+2√5)/32-(2+2√5)/32

4/32

1/8

0.125

Hope this help you