WBJEE 2020 Math Solved Paper

Given,
cos‌2‌x+7=1(2−sin‌x)
1−2sin2x+7=2a−a‌sin‌x
⇒2sin2x−a‌sin‌x+(2a−8)=0
This is a quadratic equation in sin‌x.
Using the quadratic formula,
sin‌x=[a±√{(−a)2−8(2a−3)}]∕(2×2)
=[a±(a−8)]∕4
sin‌x=[a+(a−8)]∕4,sin‌x=[a−(a−8)]∕4
sin‌x=(2a−8)∕4,sin‌x=8∕4
sin‌x=(a−4)∕2,sin‌x=2, is not possible
Since we know that −1≤sin‌x≤1
Therefore, −1≤(a−4)∕2≤1
Multiplying by 2 ,
−2≤a−4≤2
Adding 4
2≤a≤6