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Question

If  sin2x  + cos2y = 2 sec2z, find the value of cos2x + sin2y+2sin2z.


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Solution

Maximum value of sin2x and cos2y is one. Minimum value of sec2z is one and minimum value of 2sec2z is two.

So we have.

sin2x + cos2y ≤ 2 and sin2x + cos2y = 2 sec2z ≥ 2


sin2x + cos2y = 2 
This means each of the values sin2x, cos2y and sec2z is equal to one.

sin2x = 1 cos2x = 0

cos2y = 1 sin2 y = 0

sec2z = 1 cos2z = 1 sin2z = 0 
cos2x + sin2 y +2 sin2 z=0+0+ 2 x 0

=0 


Mathematics

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