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Question

2 sin2 β+4 cos(α+β) sin α sin β+cos 2(α+β)=

A
sin 2α
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B
cos 2β
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C
cos 2α
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D
sin 2β
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Solution

The correct option is C cos 2α
cos 2(α+β)=2 cos2(α+β)1, 2 sin2 β=1cos 2β
L.H.S.
=cos 2β+2 cos(α+β)[2 sin α sin β+cos(α+β)]
=cos 2β+2 cos(α+β)cos(α+β)
=cos 2β+(cos 2α+cos 2β)=cos 2α.


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