Question

If sin Ө + cos Ө = √2sin (90° – Ө), show that cot Ө = √2 + 1

Answer 1

Answer:

Step-by-step explanation:

was it help full

Answer 2

Given :

$\sin \theta+\cos \theta=\sqrt{2}\sin(90^\circ-\theta)$

To prove : $\cot \theta=\sqrt{2}+1$

Solution :

As we know that

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

So, we get that :

$\tan \theta=\sqrt{2}-1\\\\So,\\\\\cot \theta=\dfrac{1}{\sqrt{2}-1}=\dfrac{\sqrt{2}-1}{\sqrt{2}^2-1}=\sqrt{2}+1$

Hence, proved.