The value of 2 -, when 0° < θ < 90° is equal to:
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 2 - secθ - tanθ
tanθ = sinθ/cosθ
cotθ = 1/tanθ
cos2θ = 1 - sin2θ
Substituting the value of cotθ as 1/tanθ -
= 2 - √[(cotθ + cosθ)/(cotθ - cosθ)]
= 2 - √[(1/tanθ + cosθ)/(1/tanθ - cosθ)]
= 2 - √[(1 + sinθ)/(1 - sinθ)]
Rationalizing √[(1 + sinθ)/(1 - sinθ)], we get -
= 2 - √[(1 + sinθ)2/(1 - sin2θ)]
= 2 - √[(1 + sinθ)2/(cos2θ)]
= 2 - I1 + sinθI/cosθ
= 2 - 1/cosθ - tanθ
= 2 - secθ - tanθ