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Question

The sides a,b,c of ABC, are in A.P.If cosα=ab+c,cosβ=bc+a,cosγ=ca+b then tan2α2+tan2γ2=

A
1
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B
12
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C
13
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D
23
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Solution

The correct option is D 23
Given:a,b,c are in A.P
2b=a+c
cosα1=ab+c
By componendo-dividendo rule, we have
1cosα1+cosα=b+cab+c+a
tan2α2=b+ca3b where a+c=2b
cosγ1=ca+b
By componendo-dividendo rule, we have
1cosγ1+cosγ=a+bca+b+cwhere a+c=2b
tan2γ2=a+bc3b
tan2α2+tan2β2=b+ca+a+bc3b=2b3b=23

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