Question

solve it with correct option and proper solution

Answer 1

Hey Mate !

Here is your solution :

Given,

∆ABC is right angled at B.

So,

AC = Hypotenuse

AB and BC are are another two sides.

For <A ,

AB = Adjacent side

BC = Opposite side

Given,

=> AB : AC = 1 : √2

=> AB / AC = 1/√2

=> Adjacent side / Hypotenuse = 1 /√2

=> cos A = 1/√2

Using formula ,

=> tan A = sin A / cos A

Squaring both sides ,

=> tan²A = sin²A / cos²A

Using identity :

=> sin²A = ( 1 - cos²A )

=> tan²A = ( 1 - cos²A) / cos²A

By putting the value of cos A,

=> tan²A = [ 1 - ( 1/√2 )² ] / ( 1/√2 )²

=> tan²A = [ 1 - ( 1/2 ) ] / ( 1/2 )

=> tan²A = ( 1/2 ) ÷ ( 1/2 )

=> tan²A = 1

=> tan A = √1

=> tan A = ±1

As the distance can't be in negative , therefore tan A = 1.

Now,

= 2 tan A ÷ ( 1 - tan²A )

By putting the value of tan A ,

= ( 2 × 1) ÷ [ 1 - ( 1 )² ]

= ( 2 ) ÷ ( 1 - 1 )

= ( 2 ) ÷ 0 ( Undefined )

Hence, the required answer is :

Option ( d ) undefined.

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Hope it helps !! ^_^

Answer 2

Hi ...dear...

here is your answer...!!!
first of we need to find angles A ...
here is ratio of two sides and one angle (which is right angle ) B is given so we can apply the sine rule !!!......see picture ! ...

hope this helps you!!
Regards Brainly Star Community
#shubhendu