lim x → (π)/2 (tan ²x((2 sin ²x + 3 sin x + 4)^(1/2) - (sin ²x + 6 sin x + 2)^(1/2))) is equal to

Limit, Continuity and Differentiability: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jun, Evening shift · Q4293

JEE Main 202225 Jun, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

\mathop {\lim }\limits_{x \to {\pi \over 2}} \left( {{{\tan }^2}x\left( {{{(2{{\sin }^2}x + 3\sin x + 4)}^{{1 \over 2}}} - {{({{\sin }^2}x + 6\sin x + 2)}^{{1 \over 2}}}} \right)} \right)

is equal to

JEE Main 2022 · 25 Jun, Evening shift · Q4293

JEE Main 202225 Jun, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

\mathop {\lim }\limits_{x \to {\pi \over 2}} \left( {{{\tan }^2}x\left( {{{(2{{\sin }^2}x + 3\sin x + 4)}^{{1 \over 2}}} - {{({{\sin }^2}x + 6\sin x + 2)}^{{1 \over 2}}}} \right)} \right)

is equal to