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If M and m denote maximum and minimum value of (49cos 2 X +sin 2 x) 1/2 + (49sin 2 x+cos 2 x) 1/2 then find the value of (M+m). Thanks in advance.please solve it fast.

If M and m denote maximum and minimum value of (49cos2X +sin2x)1/2 + (49sin2x+cos2x)1/2 then find the value of (M+m).     Thanks in advance.please solve it fast.

Grade:11

1 Answers

Snehal Jadhav
54 Points
5 years ago
In this question we use a easy trigonometric property:
sin2x+cos2x=1
And, then we use the maximum and minimum values possible for cos2x which are 1(one) and 0(zero) respectively.
M-maximum value
M=max{[48cos2x +(cos2x+sin2x)]1/2}
 
M=max{[48cos2x + 1]1/2}
 
maxmimum value of cos2x is 1
M=(48(1) + 1)½
 
M=(49)½
 
M=7
m-minimum value
m=min{[48cos2x +(cos2x+sin2x)]1/2}
 
m=min{[48cos2x + 1]1/2}
 
minimum value of cos2x is 0
m=(48(0)+1)1/2
 
m=1
 
The value of M+m is 8.
 

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