Evaluate -sin 9 x -sin x dxA- sin 2 x -2-sin 4 x -4-sin 6 x -6-sin 8 x -8- CB- x -2sin 2 x -2-sin 4 x -4-sin 6 x -6-sin 8 x -8- CC- 1-4log e -tan x -2sin 9 x - CD- 1-2log e -tan x -2sin 9 x - C

The correct option is B x+2 (sin2x2+sin4x4+sin6x6+sin8x8) + C∫sin9xsin xdx = ∫(sin9x sin7x)+(sin7x sin5x)+ ⋯ +(sin3x sin x )+(sin x)sin x dx =x+2 (sin2x2+si ...

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

Byju's Answer

Standard XII

Mathematics

Standard Formulae - 1

Evaluate ∫sin...

Question

$Evaluate \int \frac{sin 9 x}{sin x} d x$

(\frac{sin 2 x}{2} + \frac{sin 4 x}{4} + \frac{sin 6 x}{6} + \frac{sin 8 x}{8}) + C

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

x + 2 (\frac{sin 2 x}{2} + \frac{sin 4 x}{4} + \frac{sin 6 x}{6} + \frac{sin 8 x}{8}) + C

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

\frac{1}{4} {log}_{e} ∣ ∣ ∣ tan \frac{x}{2} sin 9 x ∣ ∣ ∣ + C

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

\frac{1}{2} {log}_{e} ∣ ∣ ∣ tan \frac{x}{2} sin 9 x ∣ ∣ ∣ + C

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

Open in App

Solution

The correct option is B $x + 2 (\frac{sin 2 x}{2} + \frac{sin 4 x}{4} + \frac{sin 6 x}{6} + \frac{sin 8 x}{8}) + C$
$\int \frac{sin 9 x}{sin x} d x = \int \frac{(sin 9 x - sin 7 x) + (sin 7 x - sin 5 x) + \dots + (sin 3 x - sin x) + (sin x)}{sin x} d x = x + 2 (\frac{sin 2 x}{2} + \frac{sin 4 x}{4} + \frac{sin 6 x}{6} + \frac{sin 8 x}{8}) + C$

Suggest Corrections

Similar questions

Q. Assertion :If

e x p {{s i n^{2} x + s i n^{4} x + s i n^{6} x + . . . . . i n f} l o g_{e} 2}

satisfies the equation

x^{2} - 9 x + 8 = 0

, then the value of

\frac{c o s x}{c o s x + s i n x}

\frac{\sqrt{3} - 1}{2} (0 < x < π / 2)

Reason:

s i n^{2} x + s i n^{4} x + s i n^{6} x + . . . .

\infty = s e c^{2} x

Q. Evaluate:

lim x \to 0 \frac{sin 7 x - sin 5 x + sin 3 x - sin x}{sin 6 x - sin 4 x + sin 2 x}

Q. If

\frac{{sin}^{4} x}{2} + \frac{{cos}^{4} x}{3} = \frac{1}{5}

then

\frac{{sin}^{8} x}{8} + \frac{{cos}^{8} x}{27}

If $\frac{s i n^{4} x}{2} + \frac{c o s^{4} x}{3} = \frac{1}{5}$ , then

Q. Evaluate :

\int s i n 4 x . s i n 8 x d x

Join BYJU'S Learning Program

Evaluate ∫sin9xsinx dx

The correct option is B x+2(sin2x2+sin4x4+sin6x6+sin8x8)+C∫sin9xsin xdx=∫(sin9x−sin7x)+(sin7x−sin5x)+⋯+(sin3x−sin x)+(sin x)sin x dx=x+2(sin2x2+sin4x4+sin6x6+sin8x8)+C

$Evaluate \int \frac{sin 9 x}{sin x} d x$