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If secθ(cosθ + sinθ) = √2, then what is the value of 2sinθ/(cosθ - sinθ)?

If secθ(cosθ + sinθ) = √2, then what is the value of 2sinθ/(cosθ - sinθ)? Correct Answer √2

Simplifying the given equation,

⇒ 1 + tan θ = √2

⇒ tan θ = √2 - 1        ----(1)

Now, 2sinθ/(cosθ - sinθ)

Dividing by sinθ in both the numerator and denominator.

⇒ 2/(cotθ - 1)

Putting the value of cotθ from equation 1,

⇒ 2/

⇒ (2√2 - 2)/(1 - √2 + 1)

⇒ (2√2 - 2)/(2 - √2) = √2

∴ 2sinθ/(cosθ - sinθ) = √2

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