Question

Evaluate each of the following:
cot²30°-2cos²60°-3/4sec²45°-4sec²30°

Answer 1

Given :   cot² 30° −2cos² 60° −3/4sec² 45° – 4sec² 30°

= (√3)² - 2(1/2)² -  ¾(√2)² - 4×(2/√3)

[cot 30°= √3 , cos 60°= ½ , sec 45° = √2 ,sec 30° = 2/√3]

= 3 -  2 (¼) - ¾ × 2  -  4 × 4/3

[√3 × √3 = 3 & √2×√2 = 2]

= 3 - ½ - 3/2 - 16/3

= 3 - 4/2 -16/3

= 3 - 2 -16/3

= 1 -16/3

[By taking L.C.M of denominator. L.C.M is 3]

= ((1×3) -16)/3

= (3 - 16)/3 = -13/3

cot² 30° −2cos² 60° −3/4sec² 45° – 4sec² 30° = -13/3

Hence, cot² 30° −2cos² 60° − 3/4sec² 45° – 4sec² 30° is -13/3 .

 

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Answer 2

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