Question

sec A - tan A/sec A + tan A = 1/4,find the sin A

Answer 1

$\bold{\underline{Hey\: Mate \: ! }}$


$\bold{\underline {Revise \: formulae\: \colon}}$


$\bold{1).\: sec\: \theta = \frac{1}{cos \: \theta}}$


$\bold{2).\: tan\: \theta = \frac{sin\: \theta}{cos \: \theta}}$

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$\large{\bold{1)\: \frac{sec\: A - tan\: A }{sec\: A + tan\: A } = \frac{1}{4}}}$


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$\bold{\underline{Solution\: \colon}}$


$\implies \bold{\large{\frac{\frac{1}{cos\: A}\:-\:\frac{sin\: A}{cos\: A }}{\frac{1}{cos\: A}\:+\:\frac{sin\: A}{cos\: A }}\: = \: \frac{1}{4}}}$


$\implies \bold{\large{\frac{\frac{1\: - sin\: A}{\cancel{cos\: A }}}{\frac{1\: + \: sin\: A }{\cancel{cos\: A}}}\: = \: \frac{1}{4}}}$


$\implies \bold{\large{\frac{1\: -\: sin\: A}{1\: + \: sin\: A} \:=\: \frac{1}{4}}}$


$\bold{\underline{By\: cross\: multiplication}}$


$4[1\: -\: sin\: A ] \: = \: [1 \: + \: sin\: A]$

$4 \: - \: 4 sin\: A \: = \: 1 \: +\: sin\: A$

$4 \: - \: 1 \: = \: [4 sin\: A \: + \: sin\: A]$

$5 sin\: A \: = \: 3$

$sin\: A \: = \: \frac{3}{5}$

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$\bold{\boxed{sin\: A \: = \: \frac{3}{5}}}$

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$\bold{Thanks}$

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