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Product of Trigonometric Ratios in Terms of Their Sum

sin A+sin 2 A...

Question

$\frac{sin A + sin 2 A + sin 4 A + sin 5 A}{cos A + cos 2 A + cos 4 A + cos 5 A} =$

A

tan 2 A

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B

cot 3 A

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C

tan 3 A

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D

tan 4 A

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Solution

The correct option is C $tan 3 A$
$\frac{sin A + sin 2 A + sin 4 A + sin 5 A}{cos A + cos 2 A + cos 4 A + cos 5 A}$
$= \frac{(sin A + sin 5 A) + (sin 4 A + sin 2 A)}{(cos 5 A + cos A) + (cos 4 A + cos 2 A)}$
$= \frac{2 sin 3 A cos 2 A + 2 sin 3 A cos A}{2 cos 3 A cos 2 A + 2 cos 3 A cos A}$
$= \frac{2 sin 3 A (cos 2 A + cos A)}{2 cos 3 A (cos 2 A + cos A)}$
$= tan 3 A$

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Product of Trigonometric Ratios in Terms of Their Sum

Standard XII Mathematics

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