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Trignometry

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2 Apr 2008 14:53:05 IST

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Find all number pairs x,y that satisfy the given equation;

None

tan⁴x+tan⁴y+2cot²x.cot²y=3+sin²(X+Y); x,y(0,/2)

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Hari Shankar

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Joined: 28 Feb 2007

Posts: 2173

3 Apr 2008 10:13:36 IST

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By AM-GM Inequality

an^4 x + an^4 y + 2 cot^2 x cot^2 y geq 4

with equality occurring when $\tan^4x = \tan^4y = 1$

$ext{RHS} = 3+sin^2(x+y) leq 4$

with equality occurring when $\sin(x+y) = 1$

Hence the solution is x = y = rac{pi}{4}

rahulraj1

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3 Apr 2008 11:58:13 IST

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Thank u

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