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If sec A - tan A=4, …

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If sec A - tan A=4, THEN PROVE THAT cos A= 8/16

Posted by Rakhee Swarnkar 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 3 months ago

Now, sec A - tan A = 4........(i)
We know that
(sec A - tan A)(sec A + tan A) = 1
{tex}\Rightarrow{/tex} 4(secA + tanA) = 1
{tex}\Rightarrow{/tex} secA + tanA = {tex}\frac{1}{4}{/tex} .......(ii)
Adding (i) and (ii) we get,
2 secA = {tex}\frac{{17}}{4}{/tex}
{tex}\Rightarrow{/tex} secA = {tex}\frac{{17}}{8}{/tex}
{tex}\Rightarrow{/tex} cosA = {tex}\frac{8}{{17}}{/tex}

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