Question

if cot∅ = 7/24, then find valule of sin∅.sin∅/1+coses∅.tan∅

Answer 1

HIIII........{•^•}

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$\cot( \alpha ) = \frac{base}{perpendicular} \\ \\ acc. \: to \: your \: question \: \cot( \alpha ) = \frac{7}{24} \\ \\ by \: comparing \: base = 7units \\ perpendicular = 24units \\ \\ so \: hypo. = \sqrt{ {base}^{2} + {perpendicular}^{2} } \: \\ = \sqrt{49 + 576} = \sqrt{625} = 25units \\ \\ sin \alpha = \frac{perpendicular}{hypo} \\ \sin( \alpha ) = \frac{24}{25} \\ \\ \csc( \alpha ) = \frac{1}{ \sin( \alpha ) } = \frac{25}{24} \\ \\ \tan( \alpha ) = \frac{1}{ \cot( \alpha ) } = \frac{24}{7} \\ \\ \frac{ \sin( \alpha ) \sin( \alpha ) }{1 + \csc( \alpha ) \tan( \alpha ) } \\ \\ \frac{576}{1 + \frac{25}{7} } = \frac{576 \times7 }{32} = 18 \times 7 \\ \\ = 126$

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