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find the minimum value of the expression 1/(cos 2 (pi/4+x)+sin 2 (pi/4-x))

find the minimum value of the expression 
1/(cos2(pi/4+x)+sin2(pi/4-x))

Grade:11

1 Answers

Shashank Singh
askIITians Faculty 57 Points
4 years ago
we can write cos^2(pi/4+x)= cos^2(pi/2-(pi/4-x)= sin^2(pi/4-x)
1/(2sin^2(pi/4-x)
the value will be minimum when sin^2(pi/4-x) will be maximum that is
sin^2(pi/4-x)=1
so the minimum value is ½ [ans]

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