Question

(b) Without using tables, evaluate: 4 tan 60° sec 30° +
sin 31° sec 59° + cot 59° cot 31°
8 sin
2 30° − tan
2 45°

Answer 1

Answer:

= 4 tan 60° sec 30° +sin 31° sec 59° + cot 59° cot 31° 8 sin² 30° − tan² 45°

= 4 (sin 60/cos 60)×(1/cos 30) +(sin 31)×(1/cos 59)+ (cot 59)×tan (90-31)× 8 sin²30 - tan² 45

= 4(sin 60/cos 60)×(1/sin 60)+(sin 31)(1/sin 31)+(cot 59)(1/cot 59)(8 sin² 30- tan² 45)

= (4/cos 60) + 1 +8 sin² 30- tan² 45)