## anonymous one year ago How would you use the trigonometric subtraction formula to verify this identity:

1. anonymous

$\sin(\frac{ \pi }{ 2 }-x)=cosx$

2. zzr0ck3r

$$\sin(\alpha-\beta)= \sin(\alpha)\cos(\beta)-\sin(\beta)\cos(\alpha)$$ Using that we have $$\sin(\dfrac{\pi}{2}-x)=\sin(\dfrac{\pi}{2})\cos(x)-\sin(x)\cos(\dfrac{\pi}{2})=1*\cos(x)-\sin(x)*0=\cos(x)$$

3. anonymous

Can you explain to me

4. zzr0ck3r

which part?

5. anonymous

=1∗cos(x)−sin(x)∗0=cos(x)

6. zzr0ck3r

They said you can use this formula $\sin(\alpha-\beta)= \sin(\alpha)\cos(\beta)-\sin(\beta)\cos(\alpha)$ If we let $$\alpha=\dfrac{\pi}{2}$$ and let $$\beta=x$$ we get the above result.

7. zzr0ck3r

well what is 1*cos(x)? what is 0*sin(x)? what is cos(x) -0?

8. anonymous

Yeah , but why did you add that part ?

9. zzr0ck3r

10. anonymous

Like why is that part there

11. UnkleRhaukus
12. zzr0ck3r

I feel like there is an echo in here.