The value of tan 75° - cot 75° is equal to ______. - Mathematics

प्रश्न

The value of tan 75° - cot 75° is equal to ______.

विकल्प

$2 \sqrt{3}$
$2 + \sqrt{3}$
$2 - \sqrt{3}$
1

MCQ

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उत्तर

The value of tan 75° – cot 75° is equal to $\underset{̲}{2 \sqrt{3}}$ .

Explanation:

The given expression is tan 75° − cot 75°

= $\frac{{\sin 75}^{\circ}}{{\cos 75}^{\circ}} - \frac{{\cos 75}^{\circ}}{{\sin 75}^{\circ}}$

= $\frac{\sin^{2} 75^{\circ} - \cos^{2} 75^{\circ}}{{\cos 75}^{\circ} {\sin 75}^{\circ}}$

= $\frac{2 \sin^{2} 75^{\circ} - \cos^{2} 75^{\circ}}{2 {\cos 75}^{\circ} {\sin 75}^{\circ}}$

= $\frac{- 2 {\cos 150}^{\circ}}{{\sin 150}^{\circ}}$

= $- 2 {\cot 150}^{\circ}$

= $- 2 \cot (180^{\circ} - 30^{\circ})$

= $2 {\cot 30}^{\circ}$

= $2 \sqrt{3}$

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Trigonometric Functions of Sum and Difference of Two Angles

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Q 38 Q 37 Q 39

अध्याय 3: Trigonometric Functions - Exercise [पृष्ठ ५६]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11

अध्याय 3 Trigonometric Functions
Exercise | Q 38 | पृष्ठ ५६

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Trigonometric Functions of Sum and Difference of Two Angles

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The value of tan 75° - cot 75° is equal to ______. - Mathematics

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