MHT CET 2026 20th April Morning Shift | Inverse Trigonometric Functions Question 3 | Mathematics

If $a_1, a_2, a_3, \ldots, a_n$ are in arithmetic progression with common difference d, then $\tan\left[\tan^{-1}\left(\dfrac{d}{1 + a_1 a_2}\right) + \tan^{-1}\left(\dfrac{d}{1 + a_2 a_3}\right) + \ldots + \tan^{-1}\left(\dfrac{d}{1 + a_{n-1} a_n}\right)\right] = $ ____

$\dfrac{a_1 - a_n}{1 + a_1 a_n}$

$\dfrac{a_n - a_1}{1 - a_1 a_n}$

$\dfrac{a_n - a_1}{1 + a_1 a_n}$

$\dfrac{a_1 + a_n}{1 + a_1 a_n}$

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

If $x=\tan ^{-1}\left\{\frac{\sqrt{1+t^2}-1}{t}\right\}, y=\cos ^{-1}\left\{\frac{1-t^2}{1+t^2}\right\}, \quad$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

$\frac{1}{2}$

$\frac{1}{4}$

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

$$ \cot ^{-1}\left(2 \cdot 1^2\right)+\cot ^{-1}\left(2 \cdot 2^2\right)+\cot ^{-1}\left(2 \cdot 3^2\right)+\ldots \ldots \ldots \infty= $$

$\frac{\pi}{2}$

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{8}$

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

The value of $\tan \left[2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}\right]$ is

$\frac{5}{4}$

$\frac{5}{16}$

$\frac{-7}{17}$

$\frac{7}{17}$

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