The value of cos A cos60- A cos60- A is equal toA- cos 3 AB- 1 - 2 cos AC- 1 - 4 cos 3 AD- cos2A

The correct option is C 1/4 cos 3A cosA(cos^260^∘ sin^2A) = cosA (1/4 sin^2A) = cosA (1/4 (1 cos^2A)) = cosA ( 3/4 + cos^2A) = 1/4 cosA( 3 + 4cos^2A) = ...

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Byju's Answer

Standard XII

Mathematics

Chain Rule of Differentiation

The value of ...

Question

The value of $c o s A c o s (60^{\circ} - A) c o s (60^{\circ} + A)$ is equal to

1/2 cos A

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cos 3A

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1/4 cos 3A

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cos2A

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Solution

The correct option is C
1/4 cos 3A

$c o s A (c o s^{2} 60^{\circ} - s i n^{2} A)$

= $c o s A (\frac{1}{4} - s i n^{2} A)$ = $c o s A (\frac{1}{4} - (1 - c o s^{2} A))$

= $c o s A (- \frac{3}{4} + c o s^{2} A)$ = $\frac{1}{4} c o s A (- 3 + 4 c o s^{2} A)$

= $\frac{1}{4} (4 c o s^{3} A - 3 c o s A) = \frac{1}{4} c o s 3 A$

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The value of cosAcos(60∘−A)cos(60∘+A) is equal to

The correct option is C 1/4 cos 3A cosA(cos260∘−sin2A) = cosA(14−sin2A) = cosA(14−(1−cos2A)) = cosA(−34+cos2A) = 14cosA(−3+4cos2A) =14(4cos3A−3cosA)=14cos3A

The value of $c o s A c o s (60^{\circ} - A) c o s (60^{\circ} + A)$ is equal to