Proof of Pythagorean Identity sec²θ - tan²θ = 1 Proof of Pythagorean Identity sin²θ + cos²θ = 1Īpplying the Pythagoras theorem to the triangle, we get Let us prove each pythagorean trig identity one by one. tan θ = (opposite) / (adjancent) = b / a ⇒ cot θ = a / b.
cos θ = (adjancent)/(hypotenuse) = a / c ⇒ sec θ = c / a.sin θ = (opposite)/(hypotenuse) = b / c ⇒ csc θ = c / b.Let us first define all trigonometric ratios which are further useful in deriving Pythagorean identities in trigonometry. Let us assume that AB = c, BC = a, and CA = b for our convenience. Let us consider a right-triangle ABC that is right-angled at C. We are going to prove the Pythagorean identities using the Pythagoras theorem. i.e., each Pythagorean identity can be written in 3 forms as follows: csc 2θ - cot 2θ = 1 (which gives the relation between csc and cot)Īll Pythagorean trig identities are mentioned below together.Įach of them can be written in different forms by algebraic operations.sec 2θ - tan 2θ = 1 (which gives the relation between sec and tan).There are other two Pythagorean identities that are as follows: sin 2θ + cos 2θ = 1 (which gives the relation between sin and cos).The fundamental Pythagorean identity gives the relation between sin and cos and it is the most commonly used Pythagorean identity which says: These identities are used in solving many trigonometric problems where one trigonometric ratio is given and the other ratios are to be found. Pythagorean identities are important identities in trigonometry that are derived from the Pythagoras theorem.
0 kommentar(er)
