Introduction to Trigonometry — Part 2: Trigonometric identities: visual lesson, CBSE Class 10 Mathematics (Standard 041 / Basic 241)

Lesson

Introduction to Trigonometry, Part 2: Identities

In a right triangle with hypotenuse $1$ , the legs are $\cos A$ and $\sin A$ .

In this lesson you will

Hypotenuse $1$: the legs are $\cos A$ and $\sin A$, so $\cos^2 A + \sin^2 A = 1$.

Concept

Diagram

$AB^2 + BC^2 = AC^2$ — divide by one side squared.

In triangle $ABC$ , right-angled at $B$ : $AB^2 + BC^2 = AC^2$ . Divide every term by $AC^2$ :

\left(\dfrac{AB}{AC}\right)^2 + \left(\dfrac{BC}{AC}\right)^2 = 1 \;\Rightarrow\; \cos^2 A + \sin^2 A = 1