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Question

If α, β, γ are the angles of a triangle then [tanα^i+^j+^k,^i+tanβ^j+^k, ^i+^j+tanγ^k]

A
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B
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C
2
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D
2
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Solution

The correct option is C 2
Given that [tanα^i+^j+^k,^i+tanβ^j+^k,^i+^j+tanx^k]
=∣ ∣tanα111tanβ111tanγ∣ ∣
=tanα(tanβtanx1)1(tanγ1)+1(1tanβ)
=tanαtanβtanγtanαtanγ+1+1tanβ
=2+tanαtanβtanγtanαtanγtanβ
=2(tanαtanβtanα+tanγ+tanβ property of ΔIfα+β+μ=π)

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