Trig Identities

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(ab) = sin(a)cos(b) – cos(a)sin(b)

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

sin(π/2u) = 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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