an equivalent trigonometric expression for cos (x + π/2) is: sin x -sin x none of the above cos x
an equivalent trigonometric expression for cos (x + π/2) is: sin x -sin x none of the above cos x
Answer
Explanation:
Step1: Use cosine addition formula
$\cos(A + B)=\cos A\cos B-\sin A\sin B$. Here $A = x$ and $B=\frac{\pi}{2}$. So $\cos(x+\frac{\pi}{2})=\cos x\cos\frac{\pi}{2}-\sin x\sin\frac{\pi}{2}$.
Step2: Evaluate trig - values
We know that $\cos\frac{\pi}{2}=0$ and $\sin\frac{\pi}{2} = 1$. Substituting these values, we get $\cos(x+\frac{\pi}{2})=\cos x\times0-\sin x\times1=-\sin x$.
Answer:
B. -sin x