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प्रश्न
Prove that: `1/(sec x - tan x) - 1/(cos x) = 1/(cos x) - 1/(sec x + tan x)`
प्रमेय
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उत्तर
`1/(sec x - tan x) + 1/(sec x + tan x) = 1/(cos x) + 1/(cos x)`
LHS = `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)`
Since sec2 x − tan2 x = 1
`2 sec x = 2/(cos x)`
RHS = `1/(cos x) + 1/(cos x) = 2/(cos x)`
LHS = RHS.
Hence proved.
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