Question

If $f(x)=\left|\begin{array}{ccc}\cos (x+\alpha )& \cos (x+\beta )& \cos (x+\gamma )\\ \sin (x+\alpha )& \sin (x+\beta )& \sin (x+\gamma )\\ \sin (\beta -\gamma )& \sin (\gamma -\alpha )& \sin (\alpha -\beta )\end{array}\right|$ and $f(0)=-2$ then $\sum _{r=1}^{30}|f(r)|$ equals

• A. 2
• B. 30
• C. 60
• D. 120

Answer 1

Answer: (C)

$f^{\prime }(x)=0\Rightarrow f(x)$ is constant
$\therefore |f(1)|+|f(2)|+\dots ..+|f(30)|=60$.