Question

if sin theta=p and cos theta=q then the value of p-2p^3/2q^3-q










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Answer 1

Answer:

your solution is as follows

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Step-by-step explanation:

$to \: find : value \: of\\ \frac{p - 2p {}^{ 3} }{2q {}^{3} - q } \\ \\ given \: that : \\ sin \: θ = p \\ cos \: θ = q \\ \\ thus \: then \\ tan \: θ = \frac{p}{q} \\ \\ thus \: then \: considering \\ = \frac{p - 2p {}^{3} }{2q {}^{3} - q} \\ \\ = \frac{p(1 - 2p {}^{2} )}{q(2q {}^{2} - 1)} \\ \\ = tan \: θ \times \frac{1 - 2sin {}^{2} \: θ}{2cos {}^{2} \: θ - 1 } \\ \\ = tan \: θ \times \frac{(1 - sin { }^{2} \: θ) - sin {}^{2} \: θ }{cos {}^{2} \:θ + (cos {}^{2} θ - 1) } \\ \\ = tan \: θ \times \frac{cos {}^{2} \: θ - sin {}^{2} θ}{cos {}^{2}θ + ( - sin { }^{2} \: θ) } \\ \\ = tan \: θ \times \frac{cos {}^{2} \: θ - sin {}^{2} θ}{cos {}^{2} θ - sin { }^{2}θ } \\ \\ = tan \: θ$