Question

tomorrow for me exam please help me to solve this question...frnds​

Answer 1

Hey Aathithyas !

Answer:

5$\frac{7}{12}$ or 67/12 or 5.583

Step-by-step explanation:

Given :

$\frac{5cos^{2}60 + 4sec^{2}30 - tan^{2}45}{sin^{2}30 + cos^{2}30}$

All angles in degrees.

Formulae :

sin²θ + cos²θ = 1

sin(30°) = 1/2 = cos(60°) [Complementary Angles]

sin(60°) = (√3)/2 = cos(30°) [Again Complementary Angles]

tan(45°) = 1

sec(θ) = 1/cos(θ)

Procedure :

In the denominator,

sin²30° + cos²30°, which equals to 1.

Hence the question becomes :

5cos²60° + 4sec²30° - tan²45°

⇒ 5(cos(60°))² + 4(sec(30°))² - (tan(45°))²

⇒ 5(1/2)² + 4(1/cos(30°))² - (1)²

⇒ (5/4) + 4(2/√3)² - 1

⇒ (1/4) + 4(2/√3)²

⇒ (1/4) + 4(4/3)

⇒ (1/4) + (16/3)

⇒ (3/12) + (64/12)

⇒ 67/12

⇒ 5.5833 [Approx.]

Thanks !