Question

cos theta =21/29 find sin theta-tan theta/2tan theta
Guys plss help......​

Answer 1

$Given \: cos \theta = \frac{21}{29} \:--(1)$

$\red {\frac{ sin \theta - tan \theta }{2tan \theta }}$

$= \frac{ sin \theta - \frac{sin \theta}{cos \theta }}{\frac{2sin\theta}{cos\theta}}$

$= \frac{\frac{sin \theta cos \theta - sin \theta }{cos\theta}}{\frac{2sin\theta}{cos\theta}}$

$= \frac{sin\theta( cos \theta - 1)}{\frac{2sin\theta}{cos\theta}}$

$= \frac{cos \theta - 1}{\frac{2}{cos\theta} }$

$= \frac{1}{2} \times cos\theta ( cos\theta - 1)$

$= \frac{1}{2} \times \frac{21}{29} \Big( \frac{21}{29} - 1 \Big) \\= </p><p>\frac{21}{2 \times 29} \Big( \frac{21-29}{29} \Big) \\= \frac{21}{2 \times 29} \Big( \frac{-8}{29} \Big) \\= \frac{ - 84}{841}$

Therefore.,

$\red {\frac{ sin \theta - tan \theta }{2tan \theta }} \green {= \frac{ - 84}{841} }$

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