**Q : Which expression completes the fundamental trigonometric identity sin(π/2-u) =**

**A. -sec u **

**B. csc u **

**C . cos u **

**D. -sin u**

A: Because I see that we have sin(π/2 – u), I recognize an **angle difference identity** which says:

sin(a – b) = sin(a)cos(b) – cos(a)sin(b)

So, in our case, a = π/2 and b = u… We substitute like so:

sin(π/2 – u) = sin(π/2)cos(u) – cos(π/2)sin(u)

I know that sin(π/2) = 1 and that cos(π/2) = 0 (something you need to memorize)… So, I can simplify the equation:

sin(π/2)cos(u) – cos(π/2)sin(u) = 1*cos(u) – 0*sin(u) = cos(u)

So, the correct answer is **C.** sin(π/2 – u) = cos(u).

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wow you made it look quite simple !

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