Question

if tan √2-1 show that cot √2+1​

Answer 1

Answer:

: \cot \theta = \sqrt{2}+1cotθ=

2

+1

proof :

\tan \theta = \sqrt{2}-1tanθ=

2

−1

we know that

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

cotθ

1

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

tanθ

1

i.e

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

2

−1

1

rationalising we get

\begin{gathered}\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\end{gathered}

cotθ=

2

−1

1

×

2

+1

2

+1

cotθ=

(

2

)

2

−(1)

2

+1

cotθ=

2−1

2

+1

cotθ=

1

2

+1

cotθ=

2

+1