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Question
सिद्ध कीजिए: `1/(sec x - tan x) - 1/(cos x) = 1/(cos x) - 1/(sec x + tan x)`
Theorem
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Solution
`1/(sec x - tan x) + 1/(sec x + tan x) = 1/(cos x) + 1/(cos x)`
बायाँ पक्ष = `1/(sec x - tan x) + 1/(sec x + tan x)`
= `((sec x + tan x) + (sec x - tan x))/((sec x - tan x)(sec x + tan x))`
= `(2 sec x)/(sec^2x - tan^2x)`
इसलिए sec2 x − tan2 x = 1
`2 sec x = 2/(cos x)`
दायाँ पक्ष = `1/(cos x) + 1/(cos x) = 2/(cos x)`
बायाँ पक्ष = दायाँ पक्ष
अतः सिद्ध हुआ।
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