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Question Number 24972 by Rishabh#1 last updated on 30/Nov/17

If α, β and γ are conected by the relation

{2 \tan}^{2} α \tan^{2} β \tan^{2} γ + \tan^{2} α \tan^{2} β +

\tan^{2} β \tan^{2} γ + \tan^{2} γ \tan^{2} α = 1 then

which of these are correct (multi correct)

(A) \sin^{2} α + \sin^{2} β + \sin^{2} γ = 1

(B) \cos^{2} α + \cos^{2} β + \cos^{2} γ = 2

(C) \cos 2 α + \cos 2 β + \cos 2 γ = 1

(D) \cos (α + β) \cos (α - β) = \cos^{2} γ

Answered by ajfour last updated on 30/Nov/17

s a y 2 a b c + a b + b c + c a - 1 = 0

2 (1 + a) (1 + b) (1 + c) - (1 + a) (1 + b)

- (1 + b) (1 + c) - (1 + c) (1 + a) = 0

\Rightarrow 2 = Σ \frac{1}{1 + a}

\Rightarrow Σ \cos^{2} α = 2 (B)

a n d s o Σ (1 + \cos 2 α) = 4

Σ \cos 2 α = 1 (C)

a n d Σ (1 - \cos 2 α) = 2

\Rightarrow Σ \sin^{2} α = 1 (A)

A s \cos 2 α + \cos 2 β = 1 - \cos 2 γ

2 \cos (α + β) \cos (α - β) = 2 \cos^{2} γ

\Rightarrow (D)

S o a l l a r e c o r r e c t .

Commented by Rishabh#1 last updated on 30/Nov/17

t h a n k s a l o t . I learnt a new technique .