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Novay_Z [31]
2 years ago
5

Express sin(3theta) in terms of sin (theta)

Mathematics
2 answers:
BigorU [14]2 years ago
7 0
3∅ can be rewritten as (2∅+∅)
sin(3∅) = sin(2∅ + ∅<span>)
Opening brackets on the right hand side;
 = sin2</span>∅ cos ∅ + cos2∅sin<span>∅
</span><span>This simplifies to;
 = 2sin</span>∅cos^2∅ + sin∅ (1- 2sin^2∅<span>)
 = sin</span>∅ (2cos^2∅ + 1 - 2sin^2∅<span>)
 = sin</span>∅ (2(1 - sin^2∅) +1-2sin^2∅<span>)
 = 3sin</span>∅ - 4sin^3<span>∅</span>
tamaranim1 [39]2 years ago
5 0

First of all:-

3∅ can be called (2∅+∅)
so, sin(3∅) = sin(2∅ + ∅<span>)
Open brackets on the RHS (right hand side)
 = sin2</span>∅ cos ∅ + cos2∅sin<span>∅
</span><span>This is simplified into;
 = 2sin</span>∅cos^2∅ + sin∅ (1- 2sin^2∅<span>)
 = sin</span>∅ (2cos^2∅ + 1 - 2sin^2∅<span>)
 = sin</span>∅ (2(1 - sin^2∅) +1-2sin^2∅<span>)
 = 3sin</span>∅ - 4sin^3∅

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