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Prove that sin theeta - 2sin^3 …

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Prove that sin theeta - 2sin^3 theeta /2cos^3 theeta -cos theeta is equal to tan theeta

Posted by Khushi ?? 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

LHS = (sin{tex}\theta{/tex} - 2sin³{tex}\theta{/tex})
= sin{tex}\theta{/tex}(1 - 2sin²{tex}\theta{/tex})
RHS = (2cos³{tex}\theta{/tex} - cos{tex}\theta{/tex})tan{tex}\theta{/tex}
= cos{tex}\theta{/tex}(2cos²{tex}\theta{/tex} - 1){tex}\frac { \sin \theta } { \cos \theta }{/tex}
= [2(1 - sin²{tex}\theta{/tex}) - 1)sin{tex}\theta{/tex}
= (2 - 2sin²{tex}\theta{/tex} -1)sin{tex}\theta{/tex}
= (1 - 2sin²{tex}\theta{/tex})sin{tex}\theta{/tex}
{tex}\Rightarrow{/tex} LHS = RHS
{tex}\therefore{/tex} (sin{tex}\theta{/tex} - 2sin³{tex}\theta{/tex}) = (2cos³{tex}\theta{/tex} - cos{tex}\theta{/tex})tan{tex}\theta{/tex}

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