Question

Shamita teaches $a^2+b^2$ number of underprivileged children of her locality every Sunday, where a $cos\theta +bsin\theta =2$ and $asin\theta –bcos\theta$= 3. The number of children taught by Shamita every Sunday is

• A. 5
• B. 7
• C. 11
• D. 13

Answer 1

The correct option is D 13

$acos\theta +bsin\theta =2$ .....(i)

$asin\theta -bcos\theta =3$ ......(ii)

Squaring and then adding (i) & (ii), we get

$a^2(si{n}^2\theta +co{s}^2\theta )+b^2(si{n}^2\theta +co{s}^2\theta )+2absin\theta cos\theta -2absin\theta cos\theta =4+9$

$\Rightarrow a^2+b^2=13$ [$si{n}^2\theta +co{n}^2\theta =1$]

[From (i) and (ii)]