Question

Evaluate each of the following:
(cosec²45°sec²30°)(sin²30°+4cot²45°-sec²60°)

Answer 1

(cosec²45°. sec²30°)(sin²30°+ 4cot²45°-sec²60°) = 43/12

Step-by-step explanation:

Evaluate (cosec²45°. sec²30°)(sin²30°+ 4cot²45°-sec²60°)

Cosec 45°= √2  

Sec 30° = 2/√3  

sin 30° = 1/2

Cot 45° = 1

Sec 60° = 2

So (cosec²45°. sec²30°)(sin²30°+ 4cot²45°-sec²60°)  

  = [(√2)² * (2/√3)²] + [ (1/2)² + 4(1)² - 2²]

  = (2 + 4/3) + (1/4 + 4 - 4)

  = 10/3 + 1/4

  = (40 + 3) / 12

  = 43/12

Value of (cosec²45°. sec²30°)(sin²30°+ 4cot²45°-sec²60°) = 43/12