Solving a trigonometric equation Can someone help me to solve this problem? Find all number pairs x,y that satisfy the equation: tan^4(x) + tan^4(y) + 2 cot^2(x) cot^2(y) = 3 + sin^2(x+y)

Marilyn Cameron

Marilyn Cameron

Answered question

2022-10-31

Solving a trigonometric equation
Can someone help me to solve this problem?
Find all number pairs x,y that satisfy the equation:
tan 4 ( x ) + tan 4 ( y ) + 2 cot 2 ( x ) cot 2 ( y ) = 3 + sin 2 ( x + y )

Answer & Explanation

na1p1a2pafr

na1p1a2pafr

Beginner2022-11-01Added 16 answers

By AM-GM inequality:
( tan x ) 4 + ( tan y ) 4 + ( cot x ) 2 ( cot y ) 2 + ( cot x ) 2 ( cot y ) 2 4 3 + ( sin ( x + y ) ) 2
So the equation occurs when: sin ( x + y ) = 1 , 1, and tan x = tan y , tan y, and tan x = cot x , cot x. So tan x = 1 , 1 = tan y. You can look at cases.

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