QJEEM19Maefe3: JEE Main 2019 Mathematics - Class 12 JEEM19Maefe3 Solution: Let f(x) = log e (sin x), (0 < x < π ) and g(x) = sin –1 (e –x…

Question

Verified Solution • 2025–26 Session moderate

Let f(x) = log_e(sin x), (0 < x <

π

) and g(x) = sin^–1 (e^–x ), (x

\geq

0). If

α

is a positive real number such that a = (fog)'(

α

) and b = (fog)(

α

), then :

Accepted Answer

f(x) = ln(sin x), g(x) = sin^–1 (e^–x)

f(g(x)) = ln(sin(sin^–1 e^–x)) = -x

f(g(

α

)) = –

α

= b

As f(g(x)) = – x

∴

(f(g(x)))' = – 1

\Rightarrow

(f(g(

α

)))' = – 1 = a

∴

b = –

α

, a = – 1

∴

a

α

² - b

α

- a = -

α

² +

α

² + 1 = 1

Step-by-Step Verified Solution