Question

If $x{\cos }^{2}3\theta +y{\cos }^4\theta =16{\cos }^6\theta +9{\cos }^2\theta$ be an identity, then-

• A. $x=-1,y=24$
• B. $x=1,y=24$
• C. $x=24,y=1$
• D. $x=1,y=1$

Answer 1

Answer: (B)

$x=1,y=24$

$x(4{\cos }^3\theta -3\cos \theta {)}^2+y{\cos }^4\theta =9{\cos }^2\theta +16{\cos }^6\theta$
$\Rightarrow 9x{\cos }^2\theta +(y-24x){\cos }^4\theta +16x{\cos }^6\theta =9{\cos }^2\theta +16{\cos }^6\theta$ being an identity
$\Rightarrow 9x=9,y=24x\Rightarrow x=1,y=24$.