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Cos 10 ∘ + Sin 10 ∘ Cos 10 ∘ − Sin 10 ∘ = - Mathematics

MCQ
\[\frac{\cos 10^\circ + \sin 10^\circ}{\cos 10^\circ - \sin 10^\circ} =\]

 

Options

  •  tan 55°

  • cot 55°

  •  −tan 35°

  • −cot 35°

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Solution

\[\tan 55^\circ\]

\[\frac{\cos10^\circ + \sin10^\circ}{\cos10^\circ - \sin10^\circ}\]
\[ = \frac{1 + \tan10^\circ}{1 - \tan10^\circ} \left[\text{ Dividing the numerator and denominator by }\cos 10^\circ \right]\]
\[ = \frac{\tan45^\circ + \tan10^\circ}{1 - \tan45^\circ \times \tan10^\circ}\]
\[ = \tan(45^\circ + 10^\circ) \left[\text{ Using }\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \right]\]
\[ = \tan55^\circ\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 7 Values of Trigonometric function at sum or difference of angles
Q 11 | Page 28
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