HELP! Trig-Proving Identities

BabaCA07 · April 22nd 2006, 08:29 AM

I'm having trouble proving this problem:

sec+cot/sec=1+csc-sin

Please help!

**TD!** · April 22nd 2006, 08:48 AM

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

$<br /> \frac{{\sec x + \cot x}}{{\sec x}} = 1 + \frac{{\cot x}}{{\sec x}} = 1 + \frac{{\frac{{\cos x}}{{\sin x}}}}{{\frac{1}{{\cos x}}}} = 1 + \frac{{\cos ^2 x}}{{\sin x}}<br />$

$<br /> 1 + \frac{{\cos ^2 x}}{{\sin x}} = 1 + \frac{{1 - \sin ^2 x}}{{\sin x}} = 1 + \frac{1}{{\sin x}} - \sin x<br />$

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

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