Question

If f (x) = |(cos(x + α), cos(x + β), cos(x + γ)), (sin(x + α), sin(x + β), sin(x + γ)), (sin(β - α), sin(γ - α), sin(α - β))| and f(2) = 5,  then ∑f(r) for r∈[r=1, 20] is equal to

(A) 5

(B) 10

(C) 100

(D) None of these 

Answer 1

Answer is (C) 100

Clearly, f′(x) = 0 ⇒ f(x) = constant.

But f(2) = 5.

Therefore, f(x) = 5.

Now