Question

if sinx+cosx = root 2 cosx then find tanx

Answer 1

Answer:

tan x = √2-1

Step-by-step explanation:

sin x + cos x =√2 cos x

sin x + cos x =√2

cos x

sin x + cos x =√2

cos x cos x

tan x + 1 = √2

tan x = √2 - 1

This is your answer hope it will help you !

Answer 2

The value of tan x is √2-1

Explanation:

The given equation : $\sin x +\cos x=\sqrt{2}\cos x$

To find the value of tan x  , we divide the above equation by \cosx on both the sides , we will get

$\dfrac{\sin x +\cos x}{\cos x}=\dfrac{\sqrt{2}\cos x}{\cos x}$

$\Rightarrow\ \dfrac{\sin x}{\cos x}+\dfrac{\cos x}{\cos x}=\dfrac{\sqrt{2}}{1}$

$\Rightarrow\ \dfrac{\sin x}{\cos x}+1=\dfrac{\sqrt{2}}{1}$

$\Rightarrow\ \dfrac{\sin x}{\cos x}=\dfrac{\sqrt{2}}{1}-1$

$\Rightarrow\ \tan x=\dfrac{\sqrt{2}}{1}-1$          [∵ $\tan x=\dfrac{\sin x}{\cos x}$]

Hence, the value of tan x is √2-1 .

# Learn more :

If Sin x = Cos² x , Then write The value of Cos²x ( 1 + cos²x )​

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