Verifying trigonometric identities

PLEASE SOLVE sin x + cos x /sin x - cos x-sin x/ cos x = sec x csc x

PLEASE SOLVE sin x + cos x /sin x - cos x-sin x/ cos x = sec x csc x

Please use parentheses. What you wrote is this:


\sin x + \frac {\cos x}{\sin x} - \cos x - \frac {\sin x}{\cos x} = secx\ csc x


which is incorrect. I believe what you meant is this:


\frac {(\sin x + \cos x)}{\sin x} \ - \ \frac {(\cos x - \sin x)}{\cos x} = sec x \ csc x


As usual for working with trig identities start by converting any tanx, cotx, secx, and cscx functions to their sinx and cosx equivalents. Then it's a simple matter of combining the two fractions, simplifying, and applying the identity:

\sin ^2 x + \cos^2x = 1