UPSC CDS 2 2022 Math Paper

Quadratic formula=‌

−b±√b2−4‌ac

2a

sin‌θ= Perpendicular / Hypotenuse
Isosceles triangle: The altitude from vertex A to the base BC is the perpendicular bisector of the base BC.4sin2θ+2‌sin‌θ−1=0
⇒sin‌θ=‌

−2±√42+4

8

⇒sin‌θ=‌

−2±2√5

8

⇒sin‌θ=‌

−2+2√5

8

⇒sin‌θ=‌

√5−1

4

In △ABD
⇒sin‌θ=‌

BD

AB

‌‌(sin‌θ=P∕H)
Using equation (1)
⇒‌

b

a

=‌

√5−1

4

Now, in △ABD
⇒‌

BC

AB

=‌

2b

a

=2×‌

b

a

⇒‌

BC

AB

=(2×‌

√5−1

4

)
⇒‌

BC

AB

=‌

(√5−1)

2