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Question

Statement (1): Maximum value of sin2x + cos2y is 2

Statement (2): Maximum value of 2 sec2z is 2


A

Both the statements are correct

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B

Only (1) is correct

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C

Only (2) is correct

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D

Both the statements are wrong.

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Solution

The correct option is B

Only (1) is correct


Maximum value of sin2x + cos2y happens when sin2x attains its maximum and cos2y attains its maximum, because both are independent terms.
Maximum value of sin2x and cos2y are 1.

Maximum value of sin2x + cos2y = 1 + 1 = 2

1st statement is correct.
Now consider sec2z. we know sec2z = 1cos2z
sec2z will be maximum when value of cos2z is zero.
Maximum value of sec2z = 10 = ∞ (or not defined. But it is not equal to 1)
Statement 2 is wrong.


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