Question

If sintheta + costheta = √2costheta Then the value of tantheta is

Answer 1

Answer:

tanx=√2-1

Step-by-step explanation:

I've just replaced theta with "x" for my convenience

sinx+cosx=√2cosx

divide the equation with cosx

sinx/cosx +cosx/cosx= √2cosx/cosx

tanx+1=√2

tanx =√2-1

Answer 2

The value of $\tan \theta$is $\sqrt{2}-1.$

Step-by-step explanation:

We have,

$\sin \theta+\cos \theta=\sqrt{2} \cos \theta$    .....(1)

To find, the value of $\tan \theta=?$

Dividing both sides by $\cos \theta$ in (1), we get

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

⇒ $\dfrac{\sin \theta}{\cos \theta}} +\dfrac{\cos \theta}{\cos \theta}}=\sqrt{2}$

⇒ $\tan \theta +1=\sqrt{2}$

⇒ $\tan \theta=\sqrt{2}-1$

Hence, the value of $\tan \theta$ is $\sqrt{2}-1.$