Two angles are complementary if their sum is 90°. If the sum of two angles A and B is 90°, then ∠A and ∠B are complementary angles and each of them is complement of the other.

∠POM + ∠OPM + ∠PMO = 180°

∠POM + ∠OPM + 90° = 180°

∠POM + ∠OPM = 90°

∠OPM = 90° – ∠POM = 90° – θ

Thus, ∠OPM and ∠POM are complementary angles.

sin (90° -  θ) = cos θ

cos (90° - θ) = sin θ

tan (90° - θ) = cot θ

cot (90° - θ) = tan θ

cosec (90° - θ) = sec θ

sec (90° - θ) = cosec θ