Trigonometric Identities

When equation involving a variable is true for all values of the variable, it is called an identity.

In right angled ΔPMO,

sin θ = PM/OP

cos θ = OM/OP

Squaring and adding,

sin2θ + cos2θ = (PM/OP)2 + (OM/OP)2

= (PM2 + OM2)/OP2

= OP2/OP2 = 1

sin2θ + cos2θ = 1

Other Identities

sec2θ – tan2θ = 1 or  sec2θ = 1 + tan2θ

cosec2θ – cot2θ = 1 or  cosec2θ = 1 + cot2θ