Answer:

10

Step-by-step explanation:

Given

Without using tables , evaluate 4tan60° sec30° + sin 31°sec59° + cot59°cot 31°/8sin^2 30° - tan^2 45°

4 tan 60 sec 30 + sin 31 sec 59 + cot 59 cot 31 / 8 sin²30 - tan²45

4 tan 60 sec 30 + sin 31 sec(90 - 31) + cot 59 cot(90 - 59) / 8 sin²30 - tan²45

4 tan 60 sec 30 + sin 31 cosec 31 + cot 59 tan 59 / 8 sin²30 - tan²45

4 tan 60 sec 30 + sin 31 x 1 / sin 31 + cot 59 x 1 /cot 59 / 8 sin²30 - tan²45

4 x √3 x 2 /√3 + 1 + 1/8 x 1/4 - 1)

4 x 2 + 1 + 1

8 + 2 = 10