# Thread: Can someone solve this trigonometric identity please?

1. ## Can someone solve this trigonometric identity please?

Can someone solve this trigonometric identity please?

Any help would be greatly appreciated!
Thanks in advance!

2. $\frac{1}{\cos{6}}-\frac{cos{6}}{1+\sin{6}}$

$=\frac{(1+\sin{6})-(\cos^2{6})}{\cos{6}(1+\sin{6})}$

$=\frac{\sin^2{6}+\sin{6}}{\cos{6}(1+\sin{6})}$ Because 1-cos^2=sin^2

$=\frac{\sin{6}(1+\sin{6})}{\cos{6}(1+\sin{6})}$

$=\frac{\sin{6}}{\cos{6}}=\tan{6}$