Question

2 cosec square 30°+x. Sin square 60° - 3 tan square 30° = 10

Answer 1

Given data :

• 2 cosec² 30⁰ + x sin² 60⁰ - 3 tan² 30⁰ = 10

To find : Determine the value of x.

Solution :

➜ 2 cosec² 30⁰ + x sin² 60⁰ - 3 tan² 30⁰ = 10

➜ 2 * 1/sin² 30⁰ + x sin² 60⁰ - 3 tan² 30⁰ = 10

➜ 2 * {1/½}² + x * {√3/2}² - 3 * {1/√3}² = 10

➜ 2 * {2}² + x * 3/4 - 3 * 1/3 = 10

➜ 2 * 4 + 3x/4 - 3/3 = 10

➜ 8 + 3x/4 - 1 = 10

➜ 8 - 1 + 3x/4 = 10

➜ 7 + 3x/4 = 10

➜ 3x/4 = 10 - 7

➜ 3x/4 = 3

➜ 3x = 3 * 4

➜ 3x = 12

➜ x = 12/3

➜ x = 4

Answer : Hence, the value of x is 4.

{More info :

Trigonometric Fundamental identities :

• sin θ/cos θ = tan θ
• sec θ = 1/cos θ
• cosec θ = 1/sin θ

• sin² θ + cos² θ = 1
• 1 + tan² θ = sec² θ
• 1 + cot² θ = cosec² θ

Trigonometric ratios of special angles :

• sin 0⁰ = 0
• sin 30⁰ = 1/2
• sin 45⁰ = 1/√2
• sin 60⁰ = √3/2
• sin 90⁰ = 1

• cos 0⁰ = 1
• cos 30⁰ = √3/2
• cos 45⁰ = 1/√2
• cos 60⁰ = 1/2
• cos 90⁰ = 0

• tan 0⁰ = 0
• tan 30⁰ = 1/√3
• tan 45⁰ = 1
• tan 60⁰ = √3
• tan 90⁰ = ∞ (infinity)}

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Answer 2

Step-by-step explanation:

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