Question

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)+cosθ

This 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 1

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.