Question

If sin theta =a-1/a+1 . find the value of tan theta

Answer 1

Answer:

$\frac{a-1 }{2\sqrt{a}}$

Step-by-step explanation:

Please refer the attached picture for the step-by-step solution of the given question.

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Answer 2

Required Answer:-

Given:

• sin θ = (a - 1)/(a + 1)

To Find:

• The value of tan θ.

Solution:

Given that,

→ sin θ = (a - 1)/(a + 1)

Therefore,

→ sin²θ = [(a - 1)/(a + 1)]²

We know that,

→ sin²θ + cos²θ = 1

Therefore,

→ cos²θ = 1 - sin²θ

Substituting the value of sin²θ, we get,

→ cos²θ = 1 - (a - 1)²/(a + 1)²

→ cos²θ = [(a + 1)² - (a - 1)²][(a + 1)²]

→ cos²θ = [a² + 2a +1 - a² + 2a - 1][(a + 1)²]

→ cos²θ = 4a/(a + 1)²

→ cos θ = √[4a/(a + 1)²]

→ cos θ = (2√a)/(a + 1)

Now, we know that,

→ tan θ = sin θ/cos θ

Putting the values in the formula, we get,

→ tan θ = (a - 1)/(a + 1) ÷ (2√a)/(a + 1)

→ tan θ = (a - 1)/(a + 1) × (a + 1)/(2√a)

→ tan θ = (a - 1)/(2√a)

→ Hence, the value of tan θ is (a - 1)/(2√a)

Answer:

• tan θ = (a - 1)/(2√a)

Formula Used:

• sin²θ + cos²θ = 1
• tan θ = sin θ/cos θ