Question

Show that $\mathrm{tanx}+cotx=secx.cosecx$

Answer 1

L.H.S

$\tan x+\cot x$

Since,

$\tan x=\frac{\sin x}{\cos x}=\frac{1}{\cot x}$

$\cot x=\frac{\cos x}{\sin x}$

Thus,

$=\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}$

$=\frac{{\sin }^{2}x+{\cos }^{2}x}{\cos x\sin x}$

We know that

${\sin }^{2}x+{\cos }^{2}x=1$

Therefore,

$=\frac{1}{\cos x\sin x}$

Since,

$\sin x=\frac{1}{\cos ecx}$

$\cos x=\frac{1}{\sec x}$

Therefore,

$=\sec x\cos ecx$

Hence, proved.