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What is the value of tanθ?(a) √(1 + cos^2θ)/cosθ(b) √(1 – cos^2θ)/cosθ(c) (√(1 – cos^2θ))cosθ(d) √(1 – cos^2θ)+cosθThis question was posed to me in my homework.This interesting question is from Trigonometric Equations topic in chapter Trigonometric Functions of Mathematics – Class 11

Answer»

Right OPTION is (b) √(1 – cos^2θ)/cosθ

For EXPLANATION I would say: If AOB is a righted ANGLED TRIANGLE with ∠AOB = θ and ∠BAO = 90°

Also, consider OA = x and OB = 1

By definition, cosθ = OA/OB= x/1 = x

So, AB = √(1 – x^2)

By definition, AB/OA = √(1 – x^2)/x

= √(1 – cos^2θ)/cosθ.


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