Question

Evaluate each of the following $cot^{2} 30^{0} -2cos^{2}60^{0}-\frac{3}{4} sec^{2}45^{0}-4sec^{2}30^{0}$

Answer 1

SOLUTION :

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° = -13/3

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Evaluate :-

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

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

= 3 - 2 × 1 / 4 - 3 / 4 × 2 - 4 × 4 / 3

= 3 - 1 / 2 - 3 / 2 - 16 / 3

= ( 18 - 3 - 9 - 32 ) / 6

= - 26 / 6

= - 13 / 3

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Since ,

cot30° = √3

cos60° = 1 / 2

sec45° = √2

sec30° = 2 / √3

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