Question

pls answer me this ​

Answer 1

Required Answer:-

Given information:

• 3cos²(x) + 7sin²(a) = 4

To prove:

• cot(x) = √3

Proof:

Given,

➡ 3cos²(x) + 7sin²(x) = 4

➡ 3cos²(x) + 3sin²(x) + 4sin²(x) = 4

➡ 3{cos²(x) + sin²(x)} + 4sin²(x) = 4

As we know that,

➡sin²(x) + cos²(x) = 1

So,

➡ 3 × 1 + 4sin²(x) = 4

➡ 3 + 4sin²(x) = 4

➡ 4sin²(x) = 1

➡ sin²(x) = 1/4

➡ sin(x) = 1/2

From Trigonometry Ratio Table,

➡ sin(x) = sin(30°)

So,

x = 30°

Therefore,

cot(x)

= 1/tan(30)°

= cos(30)°/sin(30°)

= √3/2 ÷ 1/2

= √3/2 × 2

= √3

Hence,

cot(x) = √3 (Proved)

Trigonometry Ratio Table:

$\sf Trigonometric \ Values \\\ \boxed{\begin{array}{c|c|c|c|c|c} \sf Angle & 0^{\circ} & 30^{\circ} & 45^{\circ} & 60^{\circ} & 90^{\circ} \\ \sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1 \\ \cos \theta & 1 & \dfrac{\sqrt{3}}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{1}{2} & 0 \\ \tan\theta & 0 & \dfrac{1}{\sqrt{3}} & 1 & \sqrt{3} & \textsf{Not D{e}fined}\end{array}}$

Answer 2

Answer:

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