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`        1)sin 12 X SIN 48 X SIN 54 =____________	1/16 	1/32	1/8	1/4`
2 years ago

```							Dear Krisha 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]    = cos²(36)/2 - cos(36)/4. cos(36) = (1 + √5)/4.x = cos²(36)/2 - cos(36)/4    = [(1 + √5)/4]²/2 - [(1 + √5)/4]/4    = (1 + √5)²/32 - (1 + √5)/16    = (6 + 2√5)/32 - (1 + √5)/16    = (6 + 2√5)/32 - (2 + 2√5)/32    = 4/32    = 1/8 RegardsArun (askIITians forum expert)
```
2 years ago
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