The Value of Cos (36° − A) Cos (36° + A) + Cos (54° + A) Cos (54° − A) is - Mathematics

प्रश्न

The value of cos (36° − A) cos (36° + A) + cos (54° + A) cos (54° − A) is

पर्याय

sin 2A
cos 2A
cos 3A
sin 3A

MCQ

उत्तर

cos 2A

$\cos (36^{\circ} - A) \cos (36^{\circ} + A) + \cos (54^{\circ} + A) \cos (54^{\circ} - A)$

$= \cos (36^{\circ} - A) \cos (36^{\circ} + A) + \sin [90^{\circ} - (54^{\circ} + A)] \sin [90^{\circ} - (54^{\circ} - A)] [Since \sin (90^{\circ} - θ) = \cos θ]$

$= \cos (36^{\circ} - A) \cos (36^{\circ} + A) + \sin (36^{\circ} - A) \sin (36^{\circ} + A)$

$= \cos (36^{\circ} + A - 36^{\circ} + A) [Using \cos (A - B) formula]$

$= \cos 2 A$

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Trigonometric Functions of Sum and Difference of Two Angles

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Q 16 Q 15 Q 17

पाठ 7: Values of Trigonometric function at sum or difference of angles - Exercise 7.4 [पृष्ठ २८]

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आरडी शर्मा Mathematics [English] Class 11

पाठ 7 Values of Trigonometric function at sum or difference of angles
Exercise 7.4 | Q 16 | पृष्ठ २८

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Trigonometric Functions of Sum and Difference of Two Angles

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The Value of Cos (36° − A) Cos (36° + A) + Cos (54° + A) Cos (54° − A) is - Mathematics

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