Question

in a right angle triangle ABC right angled at b if the ratio of ab to ac is 1:rrot 2 then find the valu of 2tan A/ 1_tan2A
​

Answer 1

Step-by-step explanation:

The value of \frac{2\tan A}{1+tan^2A}

1+tan

2

A

2tanA

is 1.

Step-by-step explanation:

We are given that,

In right triangle ABC, the ratio AB : AC = 1 : \sqrt{2}AB:AC=1:

2

.

So, from the figure below, we get that,

\cos A=\frac{AB}{AC}=\frac{1}{\sqrt{2}}cosA=

AC

AB

=

2

1

i.e. \cos A=\frac{1}{\sqrt{2}}cosA=

2

1

\cos A=\cos 45cosA=cos45

i.e. A = 45°

So, we have,

\frac{2\tan A}{1+tan^2A}=\frac{2\tan 45}{1+tan^245}

1+tan

2

A

2tanA

=

1+tan

2

45

2tan45

i.e. \frac{2\tan A}{1+tan^2A}=\frac{2\times 1}{1+1^2}

1+tan

2

A

2tanA

=

1+1

2

2×1

i.e. \frac{2\tan A}{1+tan^2A}=\frac{2}{2}

1+tan

2

A

2tanA

=

2

2

i.e. \frac{2\tan A}{1+tan^2A}=1

1+tan

2

A

2tanA

=1

Hence, the value of \frac{2\tan A}{1+tan^2A}

1+tan

2

A

2tanA

is 1.