Question

The expression $nsi{n}^2\theta +2ncos(\theta +\alpha )sin\alpha sin\theta +cos2(\alpha +\theta )$ is independent of $\theta$, the value of n is

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is A

2

$nsi{n}^2\theta +2ncos(\theta +\alpha )sin\alpha sin\theta +cos2(\alpha +\theta )$
$nsi{n}^2\theta +ncos(\theta +\alpha )\left(cos\right(\theta -\alpha )-cos(\theta +\alpha \left)\right)+2co{s}^2(\alpha +\theta )-1$
$nsi{n}^2\theta +n(co{s}^2\theta -si{n}^2\alpha )-nco{s}^2(\theta +\alpha )+2co{s}^2(\alpha +\theta )-1$
$nsi{n}^2\theta +nco{s}^2\theta -nsi{n}^2\alpha +(2-n)co{s}^2(\theta +\alpha )-1$
$\Rightarrow n=2$