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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