Question

lf $y={\sin }^2\alpha +{\cos }^2(\alpha +\beta )+2\sin \alpha \sin \beta \cos (\alpha +\beta )$, then $\frac{d^{3}y}{d{x}^3}$ is

• A. $\frac{{\sin }^3(\alpha +\beta )}{\cos \alpha }$
• B. $\cos (\alpha +3\beta )$
• C. $0$
• D. $1$

Answer 1

Answer: (C)

$0$

From the question, we can see that ${\sin }^2\alpha +{\cos }^2(\alpha +\beta )+2\sin \alpha \sin \beta \cos (\alpha +\beta )$ is a constant.

Thus, $y$ is a constant.

Since, $\frac{d}{dt}(const.)=0$, therefore, $\frac{d^{3}y}{{dx}^3}=0$.