help to simplify cos((pi/2)-x)?

Answer 1

Since cos(a - b) = cosa cosb + sina sinb

cos((pi/2)-x)

= cos(pi/2) cosx + sin(pi/2) sinx

= 0*cosx + 1*sinx

= sinx


Alternately

|\←y
|. \
|... \
|..... \
|....... \
|_____\ ←x
↑
↑right angle

sin x = cos y But x + y = π/2 so y = π/2 - x

so sin x = cos(π/2 - x)

Or sine of an angle = cosine of its complement
So cosine of an angle = sine of its complement

Similarly secant of an angle = cosecant of its complement
So cosecant of an angle = secant of its complement

And tangent of an angle = cotangent of its complement
So cotangent of an angle = tangent of its complement

So cotrig fcn(x) = trigfcn(π/2 - x)
and trigfcn(x) = cotrigfcn(π/2 - x)

Answer 2

cos(pi/2 -x) = sin x is basic formula.
cos(pi/2 -x) = (cos pi/2)*(cos x) + (sin pi/2)*(sin x) = 0+1*sinx;

Answer 3

cos((pi/2) - x) = cos(pi/2)cos(x) + sin(pi/2)sin(x) = 0cos(x) + 1sin(x) = sin(x)

cos((pi/2) - x) = sin(x)