Question

If ݏ݊݅ߠܿ + ߠݏ݋√ = 2ܿߠݏ݋) ,ߠ =/ 90°) then the value of ݐ݊ܽߠ is

a) √2 − 1

b) √2 + 1

c) √2

d) −√2​

Answer 1

The required option (a) $\sqrt{2}-1$ is correct.

Step-by-step explanation:

We have,

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

Dividing both sides by $\cos \theta$, we get

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

⇒ $\tan \theta} +1=\sqrt{2}$

⇒$\tan \theta} =\sqrt{2}-1$

∴$\tan \theta} =\sqrt{2}-1$

Hence, the required option (a) $\sqrt{2}-1$ is correct.

You can see:

https://www.teachoo.com/10971/3130/Question-6/category/CBSE-Class-10-Sample-Paper-for-2020-Boards---Maths-Standard/

Answer 2

Answer:

The required option (a) \sqrt{2}-1 is correct.

Step-by-step explanation:

We have,

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

Dividing both sides by \cos \theta, we get

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

⇒ \tan \theta} +1=\sqrt{2}

⇒\tan \theta} =\sqrt{2}-1

∴\tan \theta} =\sqrt{2}-1

Hence, the required option (a) \sqrt{2}-1 is correct