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Question

cosα.sin(βγ)+cosβ.sin(γα)+cosγ.Sin(αβ) is equal to

A
0
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B
12
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C
1
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D
cosα.cosβ.cosγγ
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Solution

The correct option is A 0

cosαsin(βγ)+cosβsin(αγ)+cosγsin(αβ)

=cosα(sinβcosγsinγcosβ)+cosβ(sinγcosαsinαcosγ)+cosγ(sinαcosβsinβcosα)

=cosαsinβcosγcosαsinγsinβ+cosβsinγcosαcosβsinαcosγ+cosγsinαcosβcosγsinβcosα

=0
[using the trigonometric relation,sin(AB)=sinAcosBsinBcosA]

1170888_1296258_ans_94463971011940e8a7b85bc7ba8cf81c.JPG

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