Question

5 cos square 60 + 4 sec square 30 minus 10 square 45 whole divided by sin square 30 + cos square 30

Answer 1

Answer:

Step-by-step explanation

:

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Answer 2

Answer:

$Value \: of \:\\\frac{5cos^{2}60\degree+4sec^{2}30\degree-tan^{2}45\degree}{sin^{2}30\degree+cos^{2}30\degree}\\=\frac{67}{12}$

Step-by-step explanation:

$Value \: of \: \\</p><p>\frac{5cos^{2}60\degree+4sec^{2}30\degree-tan^{2}45\degree}{sin^{2}30\degree+cos^{2}30\degree}$

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We know the values of :

1)cos 60° = $\frac{1}{2}$

2) sec 30° = $\frac{2}{\sqrt{3}}$

3) tan 45° = 1

and

By Trigonometric identity:

$\boxed {sin^{2}A+cos^{2}A=1}$

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

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

= $\frac{5}{4}+\frac{16}{3}-1$

=$\frac{15+64-12}{12}$

=$\frac{15+52}{12}$

=$\frac{67}{12}$

Therefore,

$Value \: of \:\\\frac{5cos^{2}60\degree+4sec^{2}30\degree-tan^{2}45\degree}{sin^{2}30\degree+cos^{2}\degree}\\=\frac{67}{12}$

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