Question

$3si{n}^2\theta +7cos\theta sin2\theta +91co{s}^2\theta sin3\theta$ is expressed as a polynomial is $sin\theta$. Then the product of the numerical value of greatest coefficient and the highest degree in the polynomial is equal to

Answer 1

$3{\sin }^2\theta +7\cos \theta \sin 2\theta +91{\cos }^2\theta \sin 3\theta$
$=3{\sin }^2\theta +14{\cos }^2\theta \sin \theta +91(1-{\sin }^2\theta )(3\sin \theta -4{\sin }^3\theta )$
$=364{\sin }^5\theta -651{\sin }^3\theta +3{\sin }^2\theta +287\sin \theta$
So, required value =$651\times 5=3255$