The range of a R for which the function f(x) = (4a - 3)(x + log e 5) + 2(a - 7) cot (x/2) sin² (x/2), x ≠ 2n π, n N has critical points, is:

Sets, Relations and Functions: JEE Main 2021 Mathematics question

JEE Main 2021 · 16 Mar, Morning shift · Q3890

JEE Main 202116 Mar, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

The range of a

\in

R for which the function f(x) = (4a

-

3)(x + log_e 5) + 2(a

-

7) cot

\left( {{x \over 2}} \right)

sin²

\left( {{x \over 2}} \right)

, x

\ne

\pi

, n

\in

N has critical points, is :