Question

1/
sec x-tan x-1/
COS X=1/
COS X-1/ sec x + tan x


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Answer 1

LHS = 1/(sec x -tan x)-1/cos x

= sec x + tan x/(sec x - tan x)(sec x + tan x) - 1/cos x

= sec x + tan x/(sec2x - tan2x) - 1/cos x

= sec x + tan x - sec x

= tan x

RHS = 1/cos x - 1/(sec x + tan x)

= 1/cos x - (sec x - tan x)/(sec x + tan x) (sec x - tan x)

= 1/cos x - (sec x - tan x)/(sec2x - tan2x)

= sec x - (sec x - tan x)/1

= sec x - sec x + tan x

= tan x

it's your answer

Answer 2

$\frac{1}{secx - tanx} - \frac{1}{cosx} \\ \\ = secx + tanx - secx \\ \\ = secx - (secx - tanx) \\ \\ = \frac{1}{cosx} - \frac{1}{secx + tanx}$