Cot2 15- - 1-cot2 15- - 1 -

Cot^2 15^∘ 1/cot^2 15^∘ + 1 = cos^2 15^∘/sin^2 15^∘ 1/cos^2 15^∘/sin^2 15^∘ + 1 = cos^2 15^∘ sin^2 15^∘/cos^2 15^∘ + sin^2 15^∘ = cos(30^∘) = √(3)/2 ...

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Byju's Answer

Standard XIII

Mathematics

Cos(A+B)Cos(A-B)

cot2 15∘ - 1/...

Question

$\frac{c o t^{2} 15^{\circ} - 1}{c o t^{2} 15^{\circ} + 1}$ =

$\frac{1}{2}$

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$\frac{\sqrt{3}}{2}$

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$\frac{3 \sqrt{3}}{4}$

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$\sqrt{3}$

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Solution

The correct option is B
$\frac{\sqrt{3}}{2}$

$\frac{c o t^{2} 15^{\circ} - 1}{c o t^{2} 15^{\circ} + 1}$ = $\frac{\frac{c o s^{2} 15^{\circ}}{s i n^{2} 15^{\circ}} - 1}{\frac{c o s^{2} 15^{\circ}}{s i n^{2} 15^{\circ}} + 1}$

= $\frac{c o s^{2} 15^{\circ} - s i n^{2} 15^{\circ}}{c o s^{2} 15^{\circ} + s i n^{2} 15^{\circ}}$ = $c o s (30^{\circ})$ = $\frac{\sqrt{3}}{2}$

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Similar questions

⎡ ⎣ ⎛ ⎝ 1 + \frac{1}{10 + \frac{1}{10}} ⎞ ⎠ \times ⎛ ⎝ 1 + \frac{1}{10 + \frac{1}{10}} ⎞ ⎠ - ⎛ ⎝ 1 - \frac{1}{10 + \frac{1}{10}} ⎞ ⎠ \times ⎛ ⎝ 1 - \frac{1}{10 + \frac{1}{10}} ⎞ ⎠ ⎤ ⎦

\div ⎡ ⎣ ⎛ ⎝ 1 + \frac{1}{10 + \frac{1}{10}} ⎞ ⎠ + ⎛ ⎝ 1 - \frac{1}{10 + \frac{1}{10}} ⎞ ⎠ ⎤ ⎦

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cot215∘−1cot215∘+1 =

The correct option is B √32 cot215∘−1cot215∘+1 = cos215∘sin215∘−1cos215∘sin215∘+1 = cos215∘−sin215∘cos215∘+sin215∘ = cos(30∘) = √32

$\frac{c o t^{2} 15^{\circ} - 1}{c o t^{2} 15^{\circ} + 1}$ =