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Introduction to Trigonometry
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12/06/2021 1:04 pm
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Evaluate:
\(\frac{5cos^2 60° + 4sec^2 30° - tan^2 45°}{sin^2 30° + cos^2 30°}\)
1 Answer
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12/06/2021 1:09 pm
\(\frac{5cos^2 60° + 4sec^2 30° - tan^2 45°}{sin^2 30° + cos^2 30°}\)
We know that,
cos 60° = 1/2
sec 30° = 2/√3
tan 45° = 1
sin 30° = 1/2
cos 30° = √3/2
Now, substitute the values in the given problem, we get
\(\frac{5cos^2 60° + 4sec^2 30° - tan^2 45°}{sin^2 30° + cos^2 30°}\)
\(\frac{5(\frac{1}{2})^2+ 4(\frac{2}{\sqrt3})^2-1^2}{(\frac{1}{2})^2 + (\frac{\sqrt3}{2})^2}\)
= (5/4+16/3-1)/(1/4+3/4)
= (15+64-12)/12/(4/4)
= 67/12