# HELP! Trig-Proving Identities

• April 22nd 2006, 09:29 AM
BabaCA07
HELP! Trig-Proving Identities
I'm having trouble proving this problem:

sec+cot/sec=1+csc-sin

• April 22nd 2006, 09:48 AM
TD!
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 :)

$
\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}}
$

$
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.