Question

If tan theta equal to root2-1,show that cot theta equal to root2+1

Answer 1

Answer:

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Answer 2

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

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

proof :

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

we know that

$\tan \theta = \frac{1}{\cot \theta}$

or $\cot \theta = \frac{1}{\tan \theta}$

i.e

$\cot \theta = \frac{1}{\sqrt{2}-1}$

rationalising we get

$\cot \theta = \frac{1}{\sqrt{2}-1}\times \frac{\sqrt{2}+1}{\sqrt{2}+1}\\\\\cot \theta =\frac{\sqrt{2}+1}{(\sqrt{2})^2-(1)}\\\\\cot \theta = \frac{\sqrt{2}+1}{2-1}\\\\\cot \theta = \frac{\sqrt{2}+1}{1}\\\\\cot \theta =\sqrt{2}+1$

hence proved

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