Question

Verify the following identity:
((sin(x)+cos(x))^2 - 1) / sin(x)cos(x) = 2

Please include steps! :/ Thank you!

Answer 1

Start with the left hand side of the equation:

\[\frac{ (\sin x+cosx)^2-1}{\sin x * \cos x}=\frac{\sin^2x+2*\sin x* \cos x + \cos^2x - 1}{\sin x * \cos x}\]

\[=\frac{1+2*\sin x * \cos x - 1}{ \sin x * \cos x} = \frac{2 * \sin x * \cos x }{\sin x * \cos x} = 2\]

Answer 2

The only trig identity I used was:

sin^2x+cos^2x=1