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If sec∅+tan∅=x find the value of …

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If sec∅+tan∅=x find the value of sec∅

Posted by Shobha Upadhyay 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Given: sec x + tan x = p
As we know,
{tex}sec^2 x - tan^2 x = 1{/tex}
{tex}\therefore{/tex} {tex}(sec\ x + tan\ x)(sec\ x - tan\ x) = 1 {/tex}
{tex}\Rightarrow{/tex} {tex}p(sec\ x - tan\ x) = 1 {/tex}
{tex}\Rightarrow{/tex} {tex}sec\ x - tan\ x ={/tex} {tex}\frac{1}{p}{/tex}
Thus, we have
{tex}sec\ x + tan\ x = p{/tex} and sec x - tan x = {tex}\frac{1}{p}{/tex}
{tex}\Rightarrow{/tex} (sec x + tan x) + (sec x - tan x) = p + {tex}\frac{1}{p}{/tex} and (sec x + tan x) - (sec x - tan x) = p - {tex}\frac{1}{p}{/tex}
{tex}\Rightarrow{/tex} 2 sec x = p + {tex}\frac{1}{p}{/tex} and 2 tan x = -{tex}\frac{1}{p}{/tex} {tex}\Rightarrow{/tex} sec x = {tex}\frac{p^{2}+1}{2 p}{/tex} and tan x = {tex}\frac{p^{2}-1}{2 p}{/tex}

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