I'm having trouble proving this problem:

sec+cot/sec=1+csc-sin

Please help! :)

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- Apr 22nd 2006, 08:29 AMBabaCA07HELP! Trig-Proving Identities
I'm having trouble proving this problem:

sec+cot/sec=1+csc-sin

Please help! :) - Apr 22nd 2006, 08:48 AMTD!
1) Don't post your problem twice.

2) There is no such thing as "sin", the argument is missing.

3) Don't forget brackets, your expression is wrong now.

Now, let's see :)

$\displaystyle

\frac{{\sec x + \cot x}}{{\sec x}} = 1 + \frac{{\cot x}}{{\sec x}} = 1 + \frac{{\frac{{\cos x}}{{\sin x}}}}{{\frac{1}{{\cos x}}}} = 1 + \frac{{\cos ^2 x}}{{\sin x}}

$

$\displaystyle

1 + \frac{{\cos ^2 x}}{{\sin x}} = 1 + \frac{{1 - \sin ^2 x}}{{\sin x}} = 1 + \frac{1}{{\sin x}} - \sin x

$

Since 1/sin(x) = csc(x), we have what we wanted: LHS = RHS.