MHT CET · Maths · Differentiation

If \(\mathrm{y}=\tan ^{-1}\left[\frac{4 \sin 2 x}{\cos 2 x-6 \sin ^2 x}\right]\), then \(\frac{\mathrm{dy}}{\mathrm{d} x}\) at \(x=0\) is

A \(\frac{1}{8}\)
B \(-8\)
C \(8\)
D \(-\frac{1}{8}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(8\)

Step-by-step Solution

Detailed explanation

\(\mathrm{y}=\tan ^{-1}\left[\frac{4 \sin 2 x}{\cos 2 x-6 \sin ^2 x}\right]\) \(\mathrm{y}=\tan ^{-1}\left[\frac{4 \left(\frac{2 \tan x}{1+\tan^2 x}\right)}{\left(\frac{1-\tan^2 x}{1+\tan^2 x}\right)-6 \left(\frac{\tan^2 x}{1+\tan^2 x}\right)}\right]\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From MHT CET

Match column I and column II with respect to processes involved in respiration with their explanation

	Column I		Column II
i	Cellular respiration	a.	Exchange of gases \(\mathrm{O}_2\) and \(\mathrm{CO}_2\) between blood and tissue cells.
Ii	Breathing	b.	Physical process of gaseous exchange between atmospheric air and lungs
Iii	Internal respiration	c.	Gaseous exchange between alveolar air and blood capillaries.
Iv	External respiration	d.	Food is oxidized and ATP is generated.

MHT CET 2024 Medium

Explore more questions on app