If sin A = 24/25, then sec A = ………A) 7/25B) 25/7C) 24/7D) 7/24

1.	If sin A = 24/25, then sec A = ………A) 7/25B) 25/7C) 24/7D) 7/24
Answer» Correct option is: B) \(\frac{25}{7}\) Sin A = \(\frac {24}{25}\) \(\therefore\) cos A = \(\sqrt {1-sin^2A}\) = \(\sqrt{1-(\frac {24}{25})^2}\) = \(\sqrt {\frac {25^2 - 24^2}{25^2}}\) = \(\sqrt {\frac {625 - 576}{25}}\) = \(\sqrt {\frac {49}{25}} = \frac 7{25}\) \(\therefore\) Sec A = \(\frac 1{Cos\,A} = \frac {1} {\frac 7{25}} = \frac {25}7\) Correct option is: B) \(\frac{25}{7}\)

Answer»

Correct option is: B) \(\frac{25}{7}\)

Sin A = \(\frac {24}{25}\)

\(\therefore\) cos A = \(\sqrt {1-sin^2A}\)

= \(\sqrt{1-(\frac {24}{25})^2}\)

= \(\sqrt {\frac {25^2 - 24^2}{25^2}}\)

= \(\sqrt {\frac {625 - 576}{25}}\)

= \(\sqrt {\frac {49}{25}} = \frac 7{25}\)

\(\therefore\) Sec A = \(\frac 1{Cos\,A} = \frac {1} {\frac 7{25}} = \frac {25}7\)

Correct option is: B) \(\frac{25}{7}\)

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