Question

Statement (1): Maximum value of $si{n}^2$x + $co{s}^2$y is 2

Statement (2): Maximum value of 2 $se{c}^2$z is 2

• A. Both the statements are correct
• B. Only (1) is correct
• C. Only (2) is correct
• D. Both the statements are wrong.

Answer 1

The correct option is B

Only (1) is correct

Maximum value of $si{n}^2$x + $co{s}^2$y happens when $si{n}^2$x attains its maximum and $co{s}^2$y attains its maximum, because both are independent terms.
Maximum value of $si{n}^2$x and $co{s}^2$y are 1.

$\Rightarrow$ Maximum value of $si{n}^2$x + $co{s}^2$y = 1 + 1 = 2

$\Rightarrow$ 1st statement is correct.
Now consider $se{c}^2$z. we know $se{c}^2$z = $\frac{1}{co{s}^{2}z}$
$se{c}^2$z will be maximum when value of $co{s}^2$z is zero.
$\Rightarrow$ Maximum value of $se{c}^2$z = $\frac{1}{0}$ = ∞ (or not defined. But it is not equal to 1)
$\Rightarrow$ Statement 2 is wrong.