If A+B+C = π then cos(C+A) = (A) cos B (B) -cos B (C) sin B (D) -sin B

Question

If \(A+B+C=\pi\) then \(\cos (C+A)=\)

(A) \(\cos B\)

(B) \(-\cos B\)

(C) \(\sin B\)

(D) \(-\sin B\)

Answer 1

Correct option is (B) -cos B

\(A + B + C = \pi\)  

\(C + A = \pi - B\)   

\(\cos (C +A) = \cos (\pi - B)\)

Using the trigonometric identity \(\cos (\pi - \theta) = -\cos(\theta),\) we get \(\cos (C+A) = -\cos(B)\)