Question

What is the value of the expression:
3tan² 60° / 4sin² 30° sec² 60° + 5 cot²45°

a) 1/2
b) 2/3
c) 1
d) 4​

Answer 1

Answer:

c) 1

Step-by-step explanation:

3tan² 60°/ 4sin² 30° sec² 60° + 5 cot² 45°

= 3(√3×√3)/4(1/2 × 1/2)×(2×2)+5(1×1)

= 3×3 / 4(1/4)(4)+5

= 9 / 4+5

= 9/9

= 1

Hope it helps you:)

Answer 2

$\sf \bold {To\:find\::}$ Value of expression $\sf \dfrac{3tan^{2}60^{\circ}}{4sin^{2}30^{\circ} sec^{2}60^{\circ}\:+\:5cot^{2}45^{\circ}}$

$\sf \bold {Given\::}$

Using trigonometric ratio, we know;

$\sf \bullet\:tan\:60^{\circ}\:=\:\sqrt{3} \\\\\sf \bullet\:sin\:30^{\circ}\:=\:\dfrac{1}{2} \\\\\sf \bullet\:sec\:60^{\circ}\:=\:2\\\\\sf \bullet\:cot\:45^{\circ}\:=\:1$

$\sf \bold {Solution\::}$

$\sf \dfrac{3tan^{2}60^{\circ}}{4sin^{2}30^{\circ} sec^{2}60^{\circ}\:+\:5cot^{2}45^{\circ}}\\\\\sf Putting\: respective\:values\:,\:we\:get\:;\\\\\sf \implies \sf \dfrac{3(\sqrt{3}^{2})}{4(\dfrac{1}{2} ^{2})\times (2^{2})\:+\:5(1^{2})}\\\\\sf \implies \sf \dfrac{3\times 3}{4(\dfrac{1}{4} )\times (4)\:+\:5(1)}\\\\\sf \implies \dfrac{9}{1 \times (4)\:+\:5}\\\\\\\sf \implies \dfrac{9}{4\:+\:5}\\\\\\\sf \implies \dfrac{9}{9} \\\\\sf \implies 1$

$\sf \bold {ANSWER\::}\:Option\: \bold {C )\:1}$