Question

if sin0 + cos0 = root 2 cos0 0 not equal 90° then the value of tan0 is​

Answer 1

Answer:

See,

sin0 + cos0 =

$\sqrt{2} costheta$

So, sin0 = root2 cos0 - cos0

sin0= cos0 (root2 - 1)

or sin0/cos0 = root2 -1

So, tan0 =

$\sqrt{2} - 1$

Answer 2

$\tan \theta= \sqrt{2}-1$

Step-by-step explanation:

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

then

$\sin\theta +\cos\theta = \sqrt{2}\cos\theta \\\\\frac{1}{\sqrt{2}}\sin\theta +\frac{1}{\sqrt{2}}\cos\theta= \cos\theta\\\\\sin\left ( \frac{\pi}{4} \right )\sin \theta + \cos \left ( \frac{\pi}{4} \right )\cos\theta= \cos\theta\\\\\cos(\frac{\pi}{4}-\theta)= \cos\theta\\\\(\frac{\pi}{4}-\theta)= \theta\\\\\theta= \left ( \frac{\pi}{8} \right )\\\\\tan\theta = \tan \left (\frac{\pi}{8} \right )= \sqrt{2}-1$

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