Question

cot square 15 deg minus 1 divided by cot square 15 degreed plus 1​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{\dfrac{cot^215^\circ-1}{cot^215^\circ+1}}$

$\underline{\textbf{To find:}}$

$\textsf{The value of}$

$\mathsf{\dfrac{cot^215^\circ-1}{cot^215^\circ+1}}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Identity used:}}$

$\boxed{\mathsf{cos\,2A=\dfrac{1-tan^2A}{1+tan^2A}}}$

$\mathsf{Consider,}$

$\mathsf{\dfrac{cot^215^\circ-1}{cot^215^\circ+1}}$

$\mathsf{=\dfrac{\dfrac{1}{tan^215^\circ}-1}{\dfrac{1}{tan^215^\circ}+1}}$

$\mathsf{=\dfrac{\dfrac{1-tan^215^\circ}{tan^215^\circ}}{\dfrac{1+tan^215^\circ}{tan^215^\circ}}}$

$\mathsf{=\dfrac{1-tan^215^\circ}{1+tan^215^\circ}}$

$\textsf{Using the above identity, we get}$

$\mathsf{=cos\,2(15^\circ)}$

$\mathsf{=cos\,30^\circ}$

$\mathsf{=\dfrac{\sqrt{3}}{2}}$

$\implies\boxed{\mathsf{\dfrac{cot^215^\circ-1}{cot^215^\circ+1}=\dfrac{\sqrt{3}}{2}}}$

Answer 2

Given:

cot²15° - 1

cot²15 + 1

To find:

The value of

cot²15° - 1

cot²15 + 1

Solution:

Identity used:

cos 2A

Consider,

cot²15⁰ - 1

cot²15 +1.

1 tan²15° 1 1 +1

tan²15

1tan²15°

tan²15⁰ 1+tan 15°

tan²15°

1-tan²15° 1+tan²15°

Using the above identity, we get

cos 2(15%)

= cos 30⁰

√3

1tan²A

1+tan²A

V

Σ

=

cot²15 - 1

cot²15 + 1 2