Question

If $0\le x\le \frac{\pi }{2}$, then which one of the following is always correct?

• A. ${\sin }^{2}x<\frac{1}{2}$ and ${\cos }^{2}x>\frac{1}{2}$
• B. ${\sin }^{2}x>\frac{1}{2}$ and ${\cos }^{2}x<\frac{1}{2}$
• C. ${\sin }^{2}x<\frac{1}{2}$ and ${\cos }^{2}x<\frac{1}{2}$
• D. Atleast one of the ${\sin }^{2}x$, ${\cos }^{2}x$ is less than $1$

Answer 1

Answer: (A), (B)

The correct options are
A ${\sin }^{2}x<\frac{1}{2}$ and ${\cos }^{2}x>\frac{1}{2}$
B ${\sin }^{2}x>\frac{1}{2}$ and ${\cos }^{2}x<\frac{1}{2}$

$2$ if $si{n}^{2}x<\frac{1}{2}$

$\Rightarrow (1-co{s}^{2}x)<\frac{1}{2}$

$\Rightarrow co{s}^{2}x>\frac{1}{2}$

$6$ vile voles