UPSC CDS Math Trigonometric Ratios and Trigonometric Identities Questions

‌‌

cos2θ−3‌cos‌θ+2

sin2θ

=1
⇒cos2θ−3‌cos‌θ+2=1−cos2θ
⇒2cos2θ−3‌cos‌θ+1=0
⇒(2‌cos‌θ−1)(cos‌θ−1)=0
⇒2‌cos‌θ−1=0‌or‌cos‌θ−1=0
⇒cos‌θ=‌‌

1

2

‌or‌cos‌θ=1
⇒ θ = 60° and θ = 0°
But, 0 < θ < 90° (Given)
∴ θ = 60° is the only solution of the given equation.
Thus, there is only one value of θ ( 0 < θ < 90°) satisfying the given equation
Hence, statement 1 is incorrect and statement 2 is correct.