① à laide dune formule simple dangles composés, démontre que sin(x + π/2)=cos x.

Explanation:

Step1: Recall angle - sum formula

The formula for $\sin(A + B)=\sin A\cos B+\cos A\sin B$. Here $A = x$ and $B=\frac{\pi}{2}$. So, $\sin\left(x+\frac{\pi}{2}\right)=\sin x\cos\frac{\pi}{2}+\cos x\sin\frac{\pi}{2}$.

Step2: Evaluate trigonometric values

We know that $\cos\frac{\pi}{2}=0$ and $\sin\frac{\pi}{2} = 1$. Substituting these values into the above - expression: $\sin x\times0+\cos x\times1$.

Step3: Simplify the expression

$\sin x\times0+\cos x\times1=0 + \cos x=\cos x$.

Answer:

We have shown that $\sin\left(x+\frac{\pi}{2}\right)=\cos x$ using the angle - sum formula for sine.