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If \(\sec x-\tan x=\frac{1}{4}\), what is the value of (\sec x+\tan x)?यदि \(\sec x-\tan x=\frac{1}{4}\), तो (\sec x+\tan x) का मान क्या है?
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Correct answer:सही उत्तर: 44
Using the identity \(\sec^2 x-\tan^2 x=1\), we get \((\sec x-\tan x)(\sec x+\tan x)=1\). Hence \(\frac{1}{4}(\sec x+\tan x)=1\), so \(\sec x+\tan x=4\). The option \(16\) may result from incorrectly squaring \(\frac{1}{4}\). Exam tip: rewrite \(\sec^2 x-\tan^2 x=1\) as a product in such questions.पहचान \(\sec^2 x-\tan^2 x=1\) से \((\sec x-\tan x)(\sec x+\tan x)=1\) मिलता है। अतः \(\frac{1}{4}(\sec x+\tan x)=1\), इसलिए \(\sec x+\tan x=4\)। विकल्प \(16\) तब आता यदि \(\frac{1}{4}\) का गलत वर्ग किया जाए। परीक्षा टिप: ऐसे प्रश्नों में \(\sec^2 x-\tan^2 x=1\) को गुणनखंडों के रूप में लिखें।
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