Express sin(3theta) in terms of sin (theta)
2 answers:
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>
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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