T-Ratios for Angle of 45°

∠POM + ∠OPM + ∠PMO = 180°

45° + ∠OPM + 90° = 180°

∠OPM = 180° – 90° – 45° = 45°

In ΔPMO, ∠OPM = ∠POM = 45°

 

OM = PM = a units

In right triangle PMO,

OP2 = OM2 + PM2 (Pythagoras Theorem)

= a2 + a2

= 2a2

OP = √2a units

sin 45° = 1/√2

cos 45° = 1/√2

tan 45° = 1

cosec 45° = √2

sec 45° = √2

cot 45° = 1