Question

If $\alpha co{s}^{2}3\theta +\beta co{s}^4\theta =16co{s}^6\theta +9co{s}^2\theta$ is an identity then

• A. α=1, β=18
• B. α =1, β=24
• C. α =3, β=24
• D. α =4, β=2

Answer 1

The correct option is B

α =1, β=24

$\alpha {[4co{s}^3\theta -3cos\theta ]}^2+\beta co{s}^4\theta =16co{s}^6\theta +9co{s}^2\theta$

$\Rightarrow 16\alpha co{s}^6\theta +(\beta -24\alpha )co{s}^4\theta +9\alpha co{s}^2\theta$

= $16co{s}^6\theta +9co{s}^2\theta$

$\Rightarrow \alpha =1and\beta -24\alpha =0$ $\Rightarrow \alpha =1and\beta =24$