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Question
The value of (cos α + cos β)2 + (sin α + sin β)2 is ______.
Options
`2 cos^2 ((α - β)/2)`
`4 cos^2 ((α - β)/2)`
`4 sin^2 ((α - β)/2)`
`2 sin^2 ((α - β)/2)`
MCQ
Fill in the Blanks
Solution
The value of (cos α + cos β)2 + (sin α + sin β)2 is `underlinebb(4 cos^2 ((α - β)/2))`.
Explanation:
We have, (cos α + cos β)2 + (sin α + sin β)2
= cos2 α + cos2 β + 2 cos α cos β + sin2 α + sin2 β + 2 sin α sin β
= (cos2 α + sin2 α) + (cos2 β + sin2 β) + 2[cos α cos β + sin α sin β]
= 1 + 1 + 2[cos (α – β)]
= 2[1 + cos (α – β)]
= `2[2 cos^2 ((α - β)/2)]`
= `4 cos^2 ((α - β)/2)`
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Trigonometric Functions of Sum and Difference of Angles
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