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Question

Taking θ=30, verify that:

(i)sin 3θ=3 sin θ4 sin3 θ

(ii)cos 3θ=4 cos3 θ3 cos θ  [2 MARKS]


Solution

Solution: 1 Mark each

When θ=30, we have 3 θ=90

(i)sin 3 θ=sin 90=1

3 sin θ4 sin3 θ

=3 sin 304 sin3 30

=[3×124×(12)3]=(324×18)

=(3212)=1

sin 3 θ=3 sin θ4 sin3 θ


(ii)cos 3 θ=cos 90=0

4 cos3 θ3 cos θ=4 cos3 303 cos 30

=[4×(32)33×32]

=(4×338332)

=(332332)=0

cos 3 θ=4 cos3 θ3 cos θ

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