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Question

sin47+sin61sin11sin25 is equal to


A

sin36

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B

cos36

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C

sin7

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D

cos7

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Solution

The correct option is D

cos7


sin47+sin61sin11sin25sin47sin25+sin61sin11=2sin(47252)cos(47+252)+2sin(61112)cos(61+112)=2sin11 cos36+2sin25 cos36=2cos36(sin11+sin25)=2cos36{2sin(11+252)cos(11252)}=4cos36 sin18 cos7=4×(514)(5+14)cos7[cos36=5+14 and sin18514]=514cos7=cos7


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