Prove the identity. sin (π /2 − x) = sin (π/ 2 + x)

Answer 1

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

= 1 * cos x - 0 * sin x

= cos x

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

= 1 * cos x + 0 * sinx

= cos x

they are both equal to cos x, so the proof is complete