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Introduction to Trigonometry
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16/06/2021 11:42 am
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Evaluate:
\(\frac{sin θ – 2sin^3θ}{2cos^3θ-cos θ}\) = tan θ
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16/06/2021 11:44 am
\(\frac{sin θ – 2sin^3θ}{2cos^3θ-cos θ}\) = tan θ
L.H.S. = \(\frac{sin θ \; – 2sin^3θ}{2cos^3θ-\;cos θ}\)
Take sin θ as in numerator and cos θ in denominator as outside, it becomes
= [sin θ(1 – 2sin2θ)]/[cos θ(2cos2θ- 1)]
We know that sin2θ = 1-cos2θ
= sin θ[1 – 2(1-cos2θ)]/[cos θ(2cos2θ -1)]
= [sin θ(2cos2θ -1)]/[cos θ(2cos2θ -1)]
= tan θ = R.H.S.