lim x → 1 2 sin cos - 1 x - x 1 - tan cos - 1 x is equal to

Let cos − 1 x = t i.e. x = cos t So lim t → π 4 sin t − cos t 1 − tan t = lim t → π 4 − cos t = − 1 2

Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsTrigonometric and Inverse Trigonometric limitsMedium2 minPYQ_2022

MathematicsMediumsingle choice

$\lim_{x \to \frac{1}{\sqrt{2}}} \frac{\sin (\cos^{- 1} x) - x}{1 - \tan (\cos^{- 1} x)}$ is equal to

Answer:

Solution:

Let $\cos^{- 1} x = t$ i.e. $x = \cos t$

So $\lim_{t \to \frac{π}{4}} \frac{\sin t - \cos t}{1 - \tan t}$ $= \lim_{t \to \frac{π}{4}} (- \cos t) = \frac{- 1}{\sqrt{2}}$

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:Trigonometric and Inverse Trigonometric limits

⏱ 2mℹ️ Source: PYQ_2022

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