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If secθ(cosθ + sinθ) = √2, then what is the value of 2sinθ/(cosθ - sinθ)?1). 3√22). 3/√23). 1/√24). √2 |
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Answer» Simplifying the GIVEN equation, ⇒ 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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