prove this trigonometry, sine theta =cos(90-theta) how this is true with proof?

take right side
cos(90-x)=cos90.cosx+sin90sinx=
=0(cosx0+(1)(sinx)=0+sinx=sinx

cos(90 - x) =
cos90cosx + sin90sinx =
0cosx + 1sinx =
sinx

cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
cos(90-theta) = cos(90)cos(theta) + sin(90)sin(theta)
cos(90-theta) = (0) cos(theta) + (1) sin(theta)
= sin(theta)

RTP: sin(t) = cos(90-t). cos(a-b) = cos(a)cos(b) + sin(a)sin(b). Put (a,b) =(90,t). Then cos(90-t) = cos(90)cos(t) + sin(90)sin(t) = 0*cos(t) + 1*sin(t) =
sin(t). QED.

cos ( 90 - a )
cos 90 cos a + sin 90 sin a
0 + sin a = sin a

5 points