JEE Main 17 March 2021 Shift 2 Solved Paper

Given, x+2‌tan‌x=‌

π

2

⇒‌‌2‌tan‌x=‌

π

2

−x⇒tan‌x=‌

π

4

−‌

x

2

⇒‌‌tan‌x=(−‌

1

2

)x+‌

π

4

...(i)
Approach In this type of problem solving, graphical approach is best because we have to find only number of solutions, not the solution (i.e. not the value(s) of x).
Concept To find the number of solution(s) for Eq. (i), first of all, let y=tan‌x... (ii) and y=(‌

−1

2

)x+‌

π

4

... (iii) and then draw the graph of Eqs. (ii) and (iii).
Now, total number of solution(s) = Total number of point(s) of intersection of the graph (ii) and (iii).y=−‌

1

2

x+‌

π

4

intersects y=tan‌x at three distinct points in [0,2π].
∴ Total number of solutions =3