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Question

If sec x + tan x = k, cos x =

(a) k2+12k

(b) 2kk2+1

(c) kk2+1

(d) kk2-1

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Solution

(b) 2kk2+1

We have:sec x + tan x = k 11sec x + tan x = 1ksec2 x - tan2 xsec x + tan x = 1ksec x + tan xsec x - tan xsec x + tan x = 1k sec x - tan x= 1k 2Adding 1 and 2:2sec x =k + 1k2sec x =k2 + 1ksec x=k2 + 12k1cos x =k2 + 12kcos x =2kk2 + 1

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