I have tried so many times to figure out how to verify this identity! I need all the help I can get! Please help! I have tried so much! If you can tell me the steps to verify it, that would be SO HELPFUL!

SecB * cscB - 2(cosB * cscB) + cotB = tanB

Start by rewriting everything in terms of sines and cosines:

(\sec B)(\csc B) - 2(\cos B)(\csc B) + \cot B = \tan B

(\frac{1}{\cos B})(\frac{1}{\sin B}) - 2(\cos B)(\frac{1}{\sin B}) + \frac{\cos B}{\sin B} = \frac{\sin B}{\cos B}

Now let's get a common denominator for the left side:

(\frac{1}{\cos B})(\frac{1}{\sin B}) - 2(\cos B)(\frac{1}{\sin B})(\frac{\cos B}{\cos B}) + \frac{\cos B}{\sin B}(\frac{\cos B}{\cos B}) = \frac{\sin B}{\cos B}

\frac{1}{(\cos B)(\sin B)} - \frac{2\cos^2 B}{(\cos B)(\sin B)} + \frac{\cos^2 B}{(\cos B)(\sin B)} = \frac{\sin B}{\cos B}

\frac{1-2\cos^2 B+\cos^2 B}{(\cos B)(\sin B)} = \frac{\sin B}{\cos B}

\frac{1-\cos^2 B}{(\cos B)(\sin B)} = \frac{\sin B}{\cos B}

Now remember that 1-\cos^2 B = \sin^2 B, and substitute that into the numerator on the left side:

\frac{\sin^2 B}{(\cos B)(\sin B)} = \frac{\sin B}{\cos B}

Finally, just cancel out the extra sine terms in the numerator and denominator:

\frac{\sin B}{\cos B} = \frac{\sin B}{\cos B}

There you have it! Did that all make sense?