Question

sec x - 1/sec x+1 = 1-cos x/ 1+cos x

Answer 1

ANSWER : provided in the above attachment.

Here i have taken x as theata , don't get confused.

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Answer 2

$\underline \bold {Solution:-}$

We will use here the trigonometric identities

i.e, sec x = 1/ cosx

LHS

$= \frac{ \sec(x) - 1 }{ \sec(x) + 1 } \\ \\ = \frac{ \frac{1}{ \cos(x) } - 1}{ \frac{1}{ \cos(x) } + 1 } \\ \\ on \: taking \: lcm \\ \\ = \frac{ \frac{1 - \cos( x) }{ \cos(x) } }{ \frac{1 + \cos(x) }{ \cos(x) } } \\ \\ = \frac{1 - \cos(x) }{1 + \cos(x) }$

=RHS

Hence proved.