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,

sin^{2}θ + cos^{2}θ = (PM/OP)^{2} + (OM/OP)^{2}

= (PM^{2} + OM^{2})/OP^{2}

= OP^{2}/OP^{2} = 1

**sin ^{2}θ + cos^{2}θ = 1**

Other Identities

**sec ^{2}θ – tan^{2}θ = 1** or

**sec**

^{2}θ = 1 + tan^{2}θ** cosec ^{2}θ – cot^{2}θ** = 1 or

**cosec**

^{2}θ = 1 + cot^{2}θ