#### description

We know that complementary angles are the set of two angles such that their sum is equal to 90°. For example: 30° and 60° are complementary to each other as their sum is equal to 90°.The triangle ∆ABC given below, is right angled at B; ∠A and ∠C form a complementary pair.

#### notes

Recall that two angles are said to be complementary if their sum equals 90°. In

∆ABC, right-angled at B.

Let ∠A= θ

In ∆ABC,

∠A+∠B+∠C= 180° (Angle sum property)

θ+ 90°+∠C= 180°

∠C= 180°-90°-θ

∠C= (90°-θ)

Trigonometric ratios-

1) sin(90°-θ)= `"AB"/"AC"`= cosθ

2) cos(90°-θ)= `"BC"/"AC"`= sinθ

3)tan(90°-θ)= `"AB"/"BC"`= cotθ

4)cot(90°-θ)= `"BC"/"AB"`= tanθ

5)sec(90°-θ)= `"AC"/"BC"`= cosecθ

6)cosec(90°-θ)= `"AC"/"AB"`= secθ

Example: Evaluate `"sin18°"/"cos72°"`

solutioin- `"sin(90°-72°)"/"cos72°"`

sin(90°-θ)= cosθ= `"cos72°"/"cos72°"= 1`