Evaluate- limx- 0sin 7x-sin 5x-sin 3x-sin x-sin 6x-sin 4x-sin 2x

The correct option is A 1 lim_x→ 0sin 7x sin 5x+sin 3x sin xsin 6x sin 4x+sin 2x =lim_x→ 07xsin 7x7x 5xsin 5x5x+3xsin 3x3x xsin xx6xsin 6x6x 4x sin 4x ...

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Standard XII

Mathematics

Standard Formulae - 1

Evaluate: l...

Question

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

-1

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Solution

The correct option is A 1
$lim x \to 0 \frac{sin 7 x - sin 5 x + sin 3 x - sin x}{sin 6 x - sin 4 x + sin 2 x}$

$= lim x \to 0 \frac{7 x \frac{sin 7 x}{7 x} - \frac{5 x sin 5 x}{5 x} + \frac{3 x sin 3 x}{3 x} - \frac{x sin x}{x}}{\frac{6 x sin 6 x}{6 x} - \frac{4 x sin 4 x}{4 x} + \frac{2 x sin 2 x}{2 x}}$ .....As $[lim x \to 0 \frac{s i n x}{x} = 1]$

$= lim x \to 0 \frac{10 x - 6 x}{8 x - 4 x}$

$= lim x \to 0 1$

$= 1$

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Similar questions

Q. Solve the following equations:
(i)

\cos x + \cos 2 x + \cos 3 x = 0

(ii)

\cos x + \cos 3 x - \cos 2 x = 0

(iii)

\sin x + \sin 5 x = \sin 3 x

(iv)

\cos x \cos 2 x \cos 3 x = \frac{1}{4}

(v)

\cos x + \sin x = \cos 2 x + \sin 2 x

(vi)

\sin x + \sin 2 x + \sin 3 = 0

(vii)

\sin x + \sin 2 x + \sin 3 x + \sin 4 x = 0

(viii)

\sin 3 x - \sin x = 4 \cos^{2} x - 2

(ix)

\sin 2 x - \sin 4 x + \sin 6 x = 0

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

Q. Let

y = \frac{cos x + cos 2 x + cos 3 x + cos 4 x + cos 5 x + cos 6 x + cos 7 x}{sin x + sin 2 x + sin 3 x + sin 4 x + sin 5 x + sin 6 x + sin 7 x},

then which of the following hold good?

Q. The general solution of

s i n x + s i n 5 x = s i n 2 x + s i n 4 x

is:

sin x + sin 3 x + sin 5 x + sin 7 x = 4 cos x cos 2 x sin 4 x

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Evaluate: limx→0sin7x−sin5x+sin3x−sinxsin6x−sin4x+sin2x

The correct option is A 1limx→0sin7x−sin5x+sin3x−sinxsin6x−sin4x+sin2x=limx→07xsin7x7x−5xsin5x5x+3xsin3x3x−xsinxx6xsin6x6x−4xsin4x4x+2xsin2x2x.....As[limx→0sinxx=1]=limx→010x−6x8x−4x=limx→01=1

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