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The given expression sec^2 x =4xy/(x+y)^2 is true if and only if : A) x+y not equal 0B) x=y and x not = 0C ) x=yD) x and y both not equal to 0

Khushi goyal , 7 Years ago
Grade 11
anser 1 Answers
Nishchal Joshi

Last Activity: 5 Years ago

Cosec2Ѳ = 4xy / (x+y)2
 
Let cosec2Ѳ has a real value
 
Therefore, cosec2Ѳ ≥ 1
 
So, 4xy/(x+y)2 ≥ 1
 
or (x+y)2 ≤ 4xy
 
or (x+y)2 - 4xy ≤ 0
 
or (x-y)2 ≤ 0
 
This implies that x=y
 
Therefore given equation holds only if x=y
 

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