Question

SinA+CosA=√2CosA.Find TanA​

Answer 1

Answer:

this is your solution for the following information

Answer 2

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

Step-by-step explanation:

We have,

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

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

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

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

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

⇒ $\tan A +1=\sqrt{2}$

⇒ $\tan A=\sqrt{2}-1$

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