Harshit Singh
Last Activity: 4 Years ago
Given expression:
(4 tan 60° sec 30° + sin 31° sec 59° + cot 59° cot 31°) / (8 sin 30° - tan² 45°)
Step 1: Evaluate trigonometric values
Using known exact values:
tan 60° = √3, sec 30° = 2/√3
sin 30° = 1/2, tan 45° = 1, so tan² 45° = 1
sec 59° = 1/cos 59° = 1/cos (90° - 31°) = 1/sin 31° = csc 31°
cot 59° = 1/tan 59° = tan (90° - 59°) = tan 31°
cot 31° = 1/tan 31°
Step 2: Evaluate each term
First term: 4 tan 60° sec 30° = 4 × (√3) × (2/√3)
= 4 × 2
= 8
Second term: sin 31° sec 59° = sin 31° × csc 31°
= 1
Third term: cot 59° cot 31° = tan 31° × (1/tan 31°)
= 1
Now, sum up the numerator: 8 + 1 + 1 = 10
Step 3: Evaluate denominator
8 sin 30° - tan² 45°
= 8 × (1/2) - 1
= 4 - 1
= 3
Step 4: Compute the final result
= 10 / 3
= 10/3
Thus, the final answer is 10/3.
