Question

cot2x + tanx =?

show the steps

Answer 1

cot2x + tanx
cos2x / sin2x + sinx / cosx
cos2x cosx + sin2x sinx / sin2x cosx
cos(2x-x)/sin2x cosx ..........[cosxcosy + sinxsiny = cos(x-y) ]
so, cosx/sin2x cosx
1/sin2x
cosec2x

Answer 2

Answer:

$\cot 2x+\tan x=\csc 2x$  

Step-by-step explanation:

Given : Expression $\cot 2x+\tan x$

To find : The solution of the expression ?

Solution :

Expression $\cot 2x+\tan x$

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

Applying formula,

$\cos 2x=2\cos^2x-1\\\sin 2x=2\sin x\cos x$

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

Taking LCM,

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

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

We know, $\cos^2x+\sin^2 x=1$

$=\frac{2(1)-1}{2\sin x\cos x}$

$=\frac{1}{2\sin x\cos x}$

$=\frac{1}{\sin 2x}$

$=\csc 2x$

Therefore,  $\cot 2x+\tan x=\csc 2x$