Question

If tan A = √2-1 , find the value of
1) cot a
2) cos A
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Answer 1

Answer:

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□Given:

$= > tan \: a = \sqrt{2} - 1$

□To find:

• The value of cot a and cos a

□Now:

As we know tanθ=1/cotθ

Therefore

$= > cot \: a = \frac{1}{ \sqrt{2 - 1} }$

$= > cot \: a = \frac{1}{ \sqrt{2} - 1 } \times \frac{ \sqrt{2} + 1}{ \sqrt{2} + 1 }$

$= > cot \: a \: = \sqrt{2} - 1$

Hence the value of cot a =√2+1

□Here:

• We have to find the value of cos a

It is given that tanθ=\sqrt{2}-1

$= > tan \: a = \frac{p}{b}$

$= > \frac{ \sqrt{2} - 1 }{1} = \frac{p}{b}$

On comparing we get

• p=√2-1
• b=1

On applying Pythagoras' theorem:

• h²=p²+b²

We get:

$= > cos \: a = \sqrt{4 - 2 \sqrt{2} }$

Hope it helps!

Answer 2

hello...here is your solution..

see the figure in attachment..

$\cot(a) = \sqrt{2} + 1$

and

$\cos(a) = \frac{2 + \sqrt{2} }{4}$