Question

If x = 2${\sin }^2\theta$, y =$2{\cos }^2\theta +1$ then the value of (x + y) is

• A. $3$
• B. $2$
• C. $1$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $3$

$\Rightarrow$ We have, $x=2si{n}^2\theta ,y=2co{s}^2\theta +1$

$\Rightarrow$ So, $x+y$

$\Rightarrow$ $2si{n}^2\theta +2co{s}^2\theta +1$

$\Rightarrow$ $2(si{n}^2\theta +co{s}^2\theta )+1$

$\Rightarrow$ $2\left(1\right)+1$ $[\because si{n}^{2}x+co{s}^{2}x=1]$

$\Rightarrow$ $3$

$\therefore$ The value of $(x+y)=3$.