Question

if tan theta =4/3, show that√1+cos theta/1-cos theta=2​

Answer 1

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Answer 2

Step-by-step explanation:

Question -

tanθ = 4/3

To Prove -

√(1 + cosθ / 1 - cosθ) = 2

Proof -

On rationalizing the denominator -

√(1 + cosθ × 1 + cosθ)

(1 - cosθ × 1 + cosθ)

Solving -

√ (1 + cosθ)²

(1 - cos²θ)

√(1 + cosθ)²

(sin²θ)

√(1 + 1 - sin²θ + 2cosθ)

(sin²θ)

√(2 - sin²θ + 2cosθ)

(1)

2 / 1

Answer -

2