In ΔPMO and ΔP′MO,

OM = OM (Common)

∠PMO = ∠P′MO (Each = 90°)

PM = P′M (Construction)

∴ ΔPMO ≅ ΔP′MO

∴ ∠OPM = ∠OP′M = 60°

∴ OPP′ is an equilateral triangle

∴ OP = OP′

Let PM = a units

PP′ = PM + MP′ = 2a units

∴ OP = OP′ = PP′ = 2a units

In right triangle PMO,

OP^{2} = PM^{2} + OM^{2} (Pythagoras Theorem)

(2a)^{2} = a^{2} + OM^{2}

∴ OM^{2} = 3a^{2}

OM = √3a units

** sin 30° = 1/2**

**cos 30° = √3/2**

**tan 30° = 1/√3**

**cosec 30° = 2**

**sec 30° = 2/√3**

**cot 30° = √3**