Question

tanx+cotx=4, then tan^4x+cot^4x=?

Answer 1

this I your required answer.

Answer 2

Answer:

 $\tan^4 x + \cot^4 x=194$

Step-by-step explanation:

We are given $\tan x + \cot x=4$                  ....(1)

We have to find the value of $\tan^4x + \cot^4 x$

Consider, the given equation (1),

$\tan x + \cot x=4$

Squaring both side, we get  

$(\tan x + \cot x)^2=16$

Using identity $(a+b)^2=a^2+b^2+2ab$

$\tan^2 x + \cot^2 x+2\times\tan x\times\cot x=16$

Since, $\tan x =\frac{1}{\cot x}$

$\tan^2 x + \cot^2 x+2=16$

$\tan^2 x + \cot^2 x=14$  .............(2)

Again squaring (2) both sides to obtain the desired powers.

$(\tan^2 x + \cot^2 x)^2=196$

Again Using identity $(a+b)^2=a^2+b^2+2ab$

$\tan^4 x + \cot^4 x+2\times\tan^2 x\times\cot^2 x=196$

Since, $\tan x =\frac{1}{\cot x}$

$\tan^4 x + \cot^4 x+2=196$

$\tan^4 x + \cot^4 x=194$

Thus, $\tan^4 x + \cot^4 x=194$