1. Tardigrade
  2. Question
  3. Mathematics
  4. If f(x)=| cos (x+α) cos (x+β) cos (x+γ) sin (x+α) sin (x+β) sin (x+γ) sin (β-γ) sin (γ-α) sin (α-β)| and f(0)=-2 then displaystyle∑ r =130|f(r)| equals

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Q. If $f(x)=\begin{vmatrix}\cos (x+\alpha) & \cos (x+\beta) & \cos (x+\gamma) \\ \sin (x+\alpha) & \sin (x+\beta) & \sin (x+\gamma) \\ \sin (\beta-\gamma) & \sin (\gamma-\alpha) & \sin (\alpha-\beta)\end{vmatrix}$ and $f(0)=-2$ then $\displaystyle\sum_{ r =1}^{30}|f(r)|$ equals

Determinants

Solution:

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