If (cos²θ − 3cosθ + 2)/sin²θ = 1, where 0 < θ < 90°: 1. There are two values of θ satisfying the above equation. 2. θ = 60° is satisfied by the above equation. Select the correct answer using the code given below.

CDS 2016 PYQ with Answer — If (cos²θ − 3cosθ + 2)/sin²θ = 1, where 0 < θ < 90°: 1. There are two…

2016 · Q66

If (cos²θ − 3cosθ + 2)/sin²θ = 1, where 0 < θ < 90°:

1There are two values of θ satisfying the above equation.
2θ = 60° is satisfied by the above equation.

Select the correct answer using the code given below.

Elementary MathematicsTrigonometry

A1 only
B2 only
CBoth 1 and 2
DNeither 1 nor 2

Explanation

The numerator factors as (cosθ−1)(cosθ−2) and sin²θ = (1−cosθ)(1+cosθ), so the equation reduces to −(cosθ−2)/(1+cosθ) = 1, i.e. cosθ = 1/2. With 0 < θ < 90° this gives the single value θ = 60°: statement 1 false, statement 2 true — option B.