Express each one of the following in terms of trigonometric ratios of

1.	Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°(i) sin 59° + cos 56°(ii) tan 65° + cot 49°(iii) sec 76° + cosec 52°(iv) cost 78° + sec 78°
Answer» 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) sin 59° + cos 56° = sin (90° - 31°) + cos (90° - 34°) = cos 31° + sin 34° (ii) tan 65° + cot 49° = tan (90° - 25°) + cot (90° - 41°) = cot 25° + tan 41° (iii) sec 76° + cosec 52° = sec(90° - 14°) + cosec(90° - 52°) = cosec 14° + sec 38° (iv) cos 78° + sec 78° = cos (90° -78°) + sec(90° - 78°) = sin 12° + cosec 12°

Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°(i) sin 59° + cos 56°(ii) tan 65° + cot 49°(iii) sec 76° + cosec 52°(iv) cost 78° + sec 78°

Answer»

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) sin 59° + cos 56°

= sin (90° - 31°) + cos (90° - 34°)

= cos 31° + sin 34°

(ii) tan 65° + cot 49°

= tan (90° - 25°) + cot (90° - 41°)

= cot 25° + tan 41°

(iii) sec 76° + cosec 52°

= sec(90° - 14°) + cosec(90° - 52°)

= cosec 14° + sec 38°

(iv) cos 78° + sec 78°

= cos (90° -78°) + sec(90° - 78°)

= sin 12° + cosec 12°