(A) Given expression: $\tan A + \cot (180^\circ + A) + \cot (90^\circ + A) + \cot (360^\circ - A)$Using trigonometric reduction formulas:$\cot (180^\c

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(A) Given expression: $\tan A + \cot (180^\circ + A) + \cot (90^\circ + A) + \cot (360^\circ - A)$Using trigonometric reduction formulas:$\cot (180^\circ + A) = \cot A$$\cot (90^\circ + A) = -\tan A$$\cot (360^\circ - A) = -\cot A$Substituting these values into the expression:$= \tan A + \cot A - \tan A - \cot A$$= 0$

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

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Evaluate: $\tan A + \cot (180^\circ + A) + \cot (90^\circ + A) + \cot (360^\circ - A)$

A
$0$
B
$2\tan A$
C
$2\cot A$
D
$2(\tan A - \cot A)$

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Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Ratios, Functions and Identities

Subtopic

Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

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Evaluate: $\tan A + \cot (180^\circ + A) + \cot (90^\circ + A) + \cot (360^\circ - A)$

Similar Questions

Find the degree measure corresponding to the following radian measure (Use $\pi = \frac{22}{7}$):$\frac{5 \pi}{3}$ (in $^{\circ}$)

What are the polar coordinates of $(-\sqrt{3}, -1)$?

Find the angle in radians through which a pendulum swings if its length is $75 \, cm$ and the tip describes an arc of length $10 \, cm$.

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Find the degree measure corresponding to the following radian measure (Use $\pi = \frac{22}{7}$):
$\frac{5 \pi}{3}$ (in $^{\circ}$)