Question

Verify: (cosx+tanx*sinx)=secx

Answer 1

So pick a side to turn into the other to start

Answer 2

\(\cos(x) +\tan(x)\sin(x)=\\\cos(x)+\frac{\sin(x)\sin(x)}{\cos(x)}=\\\cos(x)+\frac{\sin^2(x)}{\cos(x)}=\\\cos(x)+\frac{1-\cos^2(x)}{\cos(x)}=\\\\ \frac{\cos^2(x)+1-\cos^2(x)}{\cos(x)}=\\\frac{1}{\cos(x)}=\\\sec(x)\)