Evaluate
5 Cos2 60degree + 4sec2 30degree-tan2 45 degree
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sin2 30degree + cos2 30 degree
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Step-by-step explanation:
Cos 60° = 1/2
Sec 30° = 2/√3
tan 45° = 1
sin 30° = 1/2
cos 30° = √3/2
(5cos²60° + 4sec²30° - tan²45°)/sin²30° + cos²30°
= (5(1/2)² + 4(2/√3)² - (1)²)/((1/2)² + (√3/2)²
= (5(1/4) + 4(4/3) - 1)/(1/4 + 3/4)
= (5/4 + 16/3 -1)/(1+3/4)
= (15+ 64 -12/12)/(4/4)
= (67/12)/(1)
= 67/12
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