Question

5 cos² 60 + 4 sec² 30 - tan² 45 / sin² 30 + cos² 30​

Answer 1

SOLUTION

The answer is 67/12

Given

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

NoTE

• sin²∅ + cos²∅ = 1

• tan45 = 1

• cos60 = 1/2

• sec60 = 2/√3

Now,

(Putting the values)

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

Thus,

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

Answer 2

Here's your answer :-

• Question : 5 cos² 60° + 4 sec² 30° - tan² 45° / sin² 30° + cos² 30°

• Solution : It is in the attachment.

Hope it helps!

~ A.R.M.Y ♡ ~