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Question

Assertion :If cos(βγ)+cos(γα)+cos(αβ)=32, then Reason: cosα+cosβ+cosγ=0 and sinα+sinβ+sinγ=0

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Both Assertion and Reason are incorrect
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
cos(βr)+cos(rα)+cos(α+β)=3/2
cosβcosr+sinβsinr+cosrcosα+sinr+sinα+cosαcosβ+sinαsinβ=3/2.
2cosβcosr+2sinβsinr+2cosrcosα+2sinαrsinα+cosαcosβ+2sinαsinβ=3
(cosα+cosβ+cosr)2cos2αcos2βcos2r+(sinα+sinβ+sinr)2sin2sin2αsin2βsin2r=3
(cosα+cosβ)2cos2αcos2βcos2r+(sinα+sinβ+sinr)2sin2αsin2βsin2r=3
(cosα+cosβ)2+(sinα+sinβ+sinr)2(cos2α+sin2α)(cos2β+sin2β)(cos2r+sin2r)=3
(cosα+cosβ+cosr)2+(sinα+sinβ+sinr)2111+3=0
(cosα+cosβ+cosr)2+(sinα+sinβ+sinr)2=0
cosα+cosβ+cosr=0andsinα+sinβ+sinr=0
thre both co statement ie A and B are true.

1193990_1340314_ans_ff2eb2d83e0e4faba3c398cb609f56b9.JPG

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