CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Algebra of Derivatives

If y = sin ...

Question

If $y = sin x [\frac{1}{sin x \cdot sin 2 x} + \frac{1}{sin 2 x sin 3 x} + \dots$ $+ \frac{1}{sin n x sin (n + 1) x}]$ then $\frac{d y}{d x} =$

A

cot x - cot (n + 1) x

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

(n + 1) cos e c^{2} (n + 1) x - cos e c^{2} x

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

C

{csc}^{2} x - (n + 1) cos e c^{2} (n + 1) x

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

cot x + cot (n + 1) x

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $(n + 1) cos e c^{2} (n + 1) x - cos e c^{2} x$
$\begin{matrix} y = [\frac{1}{sin x sin 2 x} + \frac{1}{sin 2 x sin 3 x} + . . . . . . . . . . . + \frac{1}{sin n x sin (n + 1) x}] y = [\frac{sin x}{sin x sin 2 x} + \frac{sin x}{sin 2 x sin 3 x} + . . . . . . . . . . . + \frac{sin x}{sin n x sin (n + 1) x}] y = [\frac{sin (2 x - x)}{sin 2 x sin x} + \frac{sin (3 x - 2 x)}{sin 3 x sin 2 x} + . . . . . . . . . . . + \frac{sin (n + 1) x - n x}{sin (n + 1) x sin n x}] y = [\frac{sin (2 x) cos x - cos 2 x sin x}{sin 2 x sin x} + \frac{sin (3 x) cos 2 x - cos 3 x sin 2 x}{sin 3 x sin 2 x} + . . . . . . . . . . . + \frac{sin (n + 1) x cos n x - cos (n + 1) x sin x}{sin (n + 1) x sin n x}] y = [\frac{sin (2 x) cos x}{sin 2 x sin x} - \frac{cos 2 x sin x}{sin 2 x sin x} + \frac{sin (3 x) cos 2 x}{sin 2 x sin x} \frac{- cos 3 x sin 2 x}{sin 3 x sin 2 x} + . . . . . . . . . . . + \frac{sin (n + 1) x cos n x}{sin (n + 1) x sin n x} - \frac{cos (n + 1) x sin x}{sin (n + 1) x sin n x}] y = [\frac{cos x}{sin x} - \frac{c o s 2 x}{sin 2 x} + \frac{c o s 2 x}{sin 2 x} - \frac{c o s 3 x}{sin 3 x} + . . . . . + \frac{cos n x}{sin n x} - \frac{cos (n + 1) x}{sin (n + 1) x}] y = [cot x - cot 2 x + cot 2 x - cot 3 x + . . . cot n x - cot (n + 1) x] y = [cot x - cot (n + 1) x] \frac{d y}{d x} = - cos e c^{2} x - (- cos e c^{2} (n + 1) x) (n + 1) \frac{d y}{d x} = (n + 1) cos e c^{2} (n + 1) x - cos e c^{2} x \end{matrix}$

Suggest Corrections

thumbs-up

0

Similar questions

y = sin x [\frac{1}{sin x . sin 2 x} + \frac{1}{sin 2 x . sin 3 x} + + \frac{1}{sin n x sin (n + 1) x}]

\frac{d y}{d x}

=

α = cos (\frac{π}{n}) + i sin (\frac{π}{n})

(x - 1) (x + 1) (x - α) (x - ¯ α) . . . (x - α^{n - 1}) (x - {¯ α}^{n - 1})

\frac{1}{x + 1} + \frac{2 x}{(x + 1) (x + 2)} + \frac{3 x^{2}}{(x + 1) (x + 2) (x + 3)} + . . . . . . . . (n

) =

?

y = {sec}^{- 1} (\frac{x + 1}{x - 1}) + {sin}^{- 1} (\frac{x - 1}{x + 1})

\frac{d y}{d x}

{tan}^{- 1} (\frac{x - 1}{x - 2}) + {tan}^{- 1} (\frac{x + 1}{x + 2}) = \frac{n}{4}

x

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Algebra of Derivatives

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Algebra of Derivatives

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon