Question

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Answer 1

Hope it helps uh!!

Keep calm and study hard

Thanks for asking

${\huge {\red {\ddot {\smile}}}}$

Answer 2

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\red{\underline \bold{To \:Prove:}} \\ \tt: \implies (cosec \: A - sin \: A)(sec \: A - cos \: A) = \frac{1}{tan \: A+ \: cot \: A}$

• According to given question :

$\bold{Solving \: L.H.S \: and \: R.H.S} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \bold{L.H.S} \\ \tt: \implies (cosec \: A - sin \:A)(sec \: A - cos \: A) \\\\ \tt\circ\:cosec\:A=\frac{1}{sin\:A}\\\\ \tt\circ\:sec\:A=\frac{1}{cos\:A} \\\\ \tt: \implies( \frac{1}{sin \: A} - sin \: A)( \frac{1}{cos \: A} - cos \: A) \\\\ \tt\circ\:sin^{2}\:A+cos^{2}\:A=1 \\\\ \tt: \implies (\frac{1 - {sin}^{2} \: A}{sin \: A})( \frac{1 - {cos}^{2} \: A }{cos \: A}) \\ \\ \tt: \implies \frac{ {cos }^{2} \: A }{sin \: A} \times \frac{ {sin}^{2} \: A }{cos \: A} \\ \\ \tt: \implies cos \:A \times sin \: A \\ \\ \: \: \: \: \: \: \: \: \: \: \bold{R.H.S} \\ \tt: \implies \frac{1}{tan \: A+ cot \: A} \\ \\ \tt: \implies \frac{1}{ \frac{sin \: A}{cos \: A} + \frac{cos \: A}{sin \: A} } \\ \\ \tt: \implies \frac{1}{ \frac{ {sin}^{2} \: A+ {cos}^{2} \: A }{cos \: A \times sin \: A} } \\ \\ \tt: \implies \frac{1}{ \frac{1}{cos \: A \times sin \: A} } \\ \\ \tt: \implies cos \: A\times sin \: A \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \green{\bold{L.H.S = R.H.S}} \\ \\ \: \: \: \: \: \: \: \: \: \:\huge{\red{\bold{Proved}}}$