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Question
Select the correct option from the given alternatives :
The value of cos A cos (60° – A) cos (60° + A) is equal to ......
Options
`1/2cos3"A"`
cos 3A
`1/4cos3"A"`
4 cos 3A
Solution
`1/4cos3"A"`
Explanation:
`cos"A"*cos(60^circ - "A")*cos(60^circ + "A")`
= (cos A) (cos 60° cos A + sin 60° sin A) . (cos 60° cos A – sin 60° sin A)
= `(cos"A")(1/2cos"A" + sqrt(3)/2sin"A")(1/2cos"A" - sqrt(3)/2sin"A")`
= `1/4cos"A"(cos^2"A" - 3sin^2"A")`
= `1/4[cos^3"A" - 3 cos "A" (1 - cos^2"A")]`
= `1/4(4cos^3"A"-3 cos "A")`
= `1/4cos3"A"`
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