Question

Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°

(i) cosec 54° + sin 72°

(ii) cot85° + cos 75°

(iii) sin 67° + cos 75°

Answer 1

sin(90° - θ) = cos θ

cos (90° - θ) = sinθ

tan (90° - θ) = cotθ

cot (90° - θ) = tanθ

sec(90° - θ) = cosecθ

cosec(90° - θ) = secθ

(i) cosec 54° + sin 54°

 = cosec(90° - 54°) + sin (90° - 72°)

= sec 36° + cos 18°

(ii) cot 85° + cos 75°

= cot (90° - 85°) + cos (90° -75°)

= tan 15° + sin15°

(iii) sin 77° + cos 75°

= sin (90° - 77°) + cos(90° - 75°)

= cos 23° + sin 15°