1.

If secθ(cosθ + sinθ) = √2, then what is the value of 2sinθ/(cosθ - sinθ)?1). 3√22). 3/√23). 1/√24). √2

Answer»

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/[1/(√2 - 1) - 1]

⇒ (2√2 - 2)/(1 - √2 + 1)

⇒ (2√2 - 2)/(2 - √2) = √2

∴ 2sinθ/(cosθ - sinθ) = √2


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