Question

If A + B + C + D = π , then the value of Σ cosA cosC − Σ sinA sinC =

(A)  −1

(B)  1

(C)  2

(D)  0

Answer 1

Correct option  (D) 0

A + B + C + D = π

A + B = π - (C + D)

cos(A + B) + cos(C + D) = 0

Σ cosA cosC − Σ sinA sinC = cos (A + C)

+ cos(C + D) + cos(A + D) + cos(B + C) + cos(B + D) + cos(A + B) = 0