Question

In right angled ∆PQR, ∠Q = 900. Therefore ∠P and ∠R are complementary angles of each other. Verify the following ratios. 

i. sin θ = cos (90 – θ) 

ii. cos θ = sin (90 – θ) 

iii. sin 30° = cos(90° – 30°) = cos 60° 

iv. cos 30° = sin(90° – 30°) = sin 60°

Answer 1

In ∆PQR, ∠Q = 90°, ∠P = θ 

∴ ∠R = 90 – θ

ii. cos θ = sin(90 – θ)

iii. Let ∠P = θ = 30° 

∴ ∠R = 90° – 30°

sin 30° = cos(90° – 30°) … [From (i) and (ii)] 

sin 30° = cos 60° 

iv. cos 30° = sin(90° – 30°) = sin 60°

∴ cos 30° = sin(90° – 30°) .,.[From (i) and (ii)] 

∴ cos 30° = sin 60°