Question

Evaluate each of the following $\frac{tan^{2}60^{0}+4cos^{2}45^{0}+3sec^{2}30^{0}+5cos^{2}90^{0}}{cosec30^{0}+sec60^{0}-cot^{2}30^{0} }$

Answer 1

SOLUTION :  

Given :  

tan² 60° + 4cos² 45° + 3sec² 30° + 5cos² 90° / cosec 30° + sec 60° −cot² 30°

= (√3)² + 4(1/√2)² + 3(2/√3)² +5(0)² / 2 + 2 - (√3)²

[tan 60° = √3 , cos 45° = 1/√2 , sec 30° = 2/√3 , cos 90°= 0  , cosec 30° = 2 ,  sec 60° = 2 , cot 30°= √3]

= 3 + 4 × ½ + 3 × 4/3 + 0 / (4 - 3)

= 3 + 2 + 4 / (1)

= 9/1 = 9

tan² 60° + 4cos² 45° + 3sec² 30° + 5cos² 90° / cosec 30° + sec 60° −cot² 30° = 9  

Hence, tan² 60° + 4cos² 45° + 3sec² 30° + 5cos² 90° / cosec 30° + sec 60° - cot² 30° = 9

HOPE THIS ANSWER WILL HELP YOU…