Question

5cos² 60⁰ + 4cos² 30⁰ - tan² 45⁰/sin² 30⁰ + cos ² 60²

Answer 1

Answer:

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

Answer 2

Answer:

Step-by-step explanation:

5cos² 60⁰ + 4cos² 30⁰ - tan² 45⁰/sin² 30⁰ + cos ² 60²

4cos² 60⁰ + cos ² 60² + 4cos² 30⁰ - tan² 45⁰/sin² 30⁰ + cos ² 3600

4cos² 60⁰  + 4cos² 30⁰ - tan² 45⁰/sin² 30⁰ + cos ² 3600 + cos ² 60°

4cos² 60⁰  + 4sin² 60⁰ - tan² 45⁰/sin² 30⁰ + cos ² 3600 + cos ² 60

4(cos² 60⁰+sin² 60⁰)  -  1/sin² 30⁰ + 1 +cos ² 60 (cos ² 3600=1)

4-1/sin² 30⁰ + 1 +cos ² 60   (cos² 60⁰+sin² 60⁰=1)

4- 1/sin² 30⁰ +1+ sin ²30     (tan45°=1)

4-1/(0.5)²+1+ (0.5)²  (sin30°=0.5)

4-4+1+(0.25)

1.25