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

Question

If f(x)=| cos (x+α) cos (x+β) cos (x+&gamma;) sin (x+α) sin (x+β) sin (x+&gamma;) sin (β-&gamma;) sin (&gamma;-α) sin (α-β)| and f(0)=-2 then displaystyle∑ r =130|f(r)| equals (A) 2 (B) 30 (C) 60 (D) 120

Tardigrade Admin · Accepted Answer

f prime(x)=0 ⇒ f(x) is constant ∴| f (1)|+| f (2)|+ ldots . .+| f (30)|=60.

Q. If $f (x) = ∣ ∣ cos (x + α) sin (x + α) sin (β - γ) cos (x + β) sin (x + β) sin (γ - α) cos (x + γ) sin (x + γ) sin (α - β) ∣ ∣$ and $f (0) = - 2$ then $r = 1 \sum 30 ∣ f (r) ∣$ equals

2

30

60

120

$f^{'} (x) = 0 \Rightarrow f (x)$ is constant
$∴ ∣ f (1) ∣ + ∣ f (2) ∣ + \dots .. + ∣ f (30) ∣ = 60$ .

Q. If f(x)=∣∣​cos(x+α)sin(x+α)sin(β−γ)​cos(x+β)sin(x+β)sin(γ−α)​cos(x+γ)sin(x+γ)sin(α−β)​∣∣​ and f(0)=−2 then r=1∑30​∣f(r)∣ equals

2

30

60

120

f′(x)=0⇒f(x) is constant ∴∣f(1)∣+∣f(2)∣+…..+∣f(30)∣=60.

Q. If $f (x) = ∣ ∣ cos (x + α) sin (x + α) sin (β - γ) cos (x + β) sin (x + β) sin (γ - α) cos (x + γ) sin (x + γ) sin (α - β) ∣ ∣$ and $f (0) = - 2$ then $r = 1 \sum 30 ∣ f (r) ∣$ equals

$f^{'} (x) = 0 \Rightarrow f (x)$ is constant
$∴ ∣ f (1) ∣ + ∣ f (2) ∣ + \dots .. + ∣ f (30) ∣ = 60$ .