Question

Show that $\tan A\cdot \sin A+\cos A=\sec A$

Answer 1

Consider LHS $=\tan A\sin A+\cos A$
$=\frac{\sin A}{\cos A}\sin A+\cos A$ $(\because \tan A=\frac{\sin A}{\cos A})$
$=\frac{{\sin }^{2}A}{\cos A}+\cos A=\frac{{\sin }^{2}A+{\cos }^{2}A}{\cos A}$ (But ${\sin }^{2}A+{\cos }^{2}A=1$)
$=\frac{1}{\cos A}=\sec A=$ RHS