Statement (1): Maximum value of sin2x + cos2y is 2
Statement (2): Maximum value of 2 sec2z is 2
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.