Question

evaluate 5cos² 60°+4sec² 30°-tan²45°​

Answer 1

Answer:

$= 463161$

99

Step-by-step explanation:

100-1

=99

Answer 2

Step-by-step explanation:

SOLUTION

The answer is 67/12

Given

$\sf \: \dfrac{5 {cos}^{2}60 + 4 {sec}^{2}30 - {tan45}^{2} }{ {sin}^{2} 30 + {cos}^{2}30 }$

(Putting the values)

$\begin{gathered} \longrightarrow \: \sf \: \dfrac{5 \times ( \frac{1}{2}) {}^{2} + 4 \times (\frac{2}{ \sqrt{3} }) {}^{2} - {1}^{2} }{1} \\ \\ \longrightarrow \: \sf \: 5 \times \dfrac{1}{4} + 4 \times \dfrac{4}{3} - 1 \\ \\ \longrightarrow \sf \: \dfrac{5}{4} + \dfrac{16}{3} - 1 \\ \\ \longrightarrow \: \sf \: \dfrac{15 + 64 - 12}{12} \\ \\ \longrightarrow \: \sf \: \dfrac{79 - 12}{12} \\ \\ \longrightarrow \sf \: \dfrac{67}{12} \end{gathered}$

Thus,

$\star \: \: \: \boxed{ \boxed{ \sf \: \dfrac{5 {cos}^{2}60 + 4 {sec}^{2}30 - {tan45}^{2} }{ {sin}^{2} 30 + {cos}^{2}30 } = \dfrac{67}{13} }}⋆$