Trigonometric Identities — Part 2: Complementary angles, proofs and expressions: visual lesson, ICSE Class 10 Mathematics

Lesson

Trigonometric Identities, Part 2

Complementary angles, proofs, and expressions: a method for every question.

In this lesson you will

Work on one side only, until it matches the other.

Concept

Use complementary-angle rules such as $\sin(90^\circ - \theta) = \cos\theta$
Prove identities by working on one side only
Use conjugates to simplify
Evaluate expressions when one ratio is given

Concept

Angles that add to $90^\circ$ are complementary. In triangle $ABC$ , $\angle A + \angle C = 90^\circ$ .

The two acute angles add to $90^\circ$: $\sin A = \dfrac{BC}{AC} = \cos C$.