Question

evaluate :5 cos² 60 + 4 cos² 30 - tan² 45 / sin²30 + cos² 60

Answer 1

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Answer 2

Answer:

Value of the expression is 6.5

Step-by-step explanation:

We have to evaluate the given expression $\frac{5cos^{2}60+4cos^{2}30-tan^{2}45}{sin^{2}30+cos^{2}60 }$

We know the value of cos 60° = $\frac{1}{2}$

sin30° = $\frac{1}{2}$

tan45° = 1

cos30° = $\frac{\sqrt{3}}{2}$

By lacing the values in the given expression

= $\frac{5(\frac{1}{2})^{2} +4(\frac{\sqrt{3}}{2})^{2}-1}{(\frac{1}{2}^{2})+(\frac{1}{2})^{2}}$

= $\frac{\frac{5}{4}+3-1}{\frac{1}{4}+\frac{1}{4}}$

= $\frac{\frac{13}{4}}{\frac{1}{2}}$

= $\frac{13}{4}\times \frac{2}{1}$

= $\frac{13}{2}$

= 6.5

Value of the expression is 6.5.

Learn more to evaluate the trigonometric expressions from https://brainly.in/question/6500797