8 Sin X 8 Cos X 2 Cos X 4 Cos X 8 is Equal to - Mathematics

प्रश्न

8 \sin \frac{x}{8} \cos \frac{x}{2} \cos \frac{x}{4} \cos \frac{x}{8}

is equal to

विकल्प

8 cos x
cos x
8 sin x
sin x

MCQ

उत्तर

sin x

$We have, 8 \sin \frac{x}{8} \cos \frac{x}{2} \cos \frac{x}{4} \cos \frac{x}{8}$
$= 4 \times (2 \sin \frac{x}{8} \cos \frac{x}{8}) \cos \frac{x}{2} \cos \frac{x}{4}$
$= 4 \times \sin \frac{x}{4} \cos \frac{x}{2} \cos \frac{x}{4}$
$= 2 \times (2 \sin \frac{x}{4} \cos \frac{x}{4}) \cos \frac{x}{2}$
$= 2 \times \sin \frac{x}{2} \cos \frac{x}{2}$
$= sin x$

shaalaa.com

Values of Trigonometric Functions at Multiples and Submultiples of an Angle

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 1 Q 13 Q 2

अध्याय 9: Values of Trigonometric function at multiples and submultiples of an angle - Exercise 9.5 [पृष्ठ ४३]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11

अध्याय 9 Values of Trigonometric function at multiples and submultiples of an angle
Exercise 9.5 | Q 1 | पृष्ठ ४३

संबंधित प्रश्न

Prove that: $\sqrt{\frac{1 - \cos 2 x}{1 + \cos 2 x}} = \tan x$

Prove that: $\cos^{2} \frac{π}{8} + \cos^{2} \frac{3 π}{8} + \cos^{2} \frac{5 π}{8} + \cos^{2} \frac{7 π}{8} = 2$

Prove that: $\sin^{2} \frac{π}{8} + \sin^{2} \frac{3 π}{8} + \sin^{2} \frac{5 π}{8} + \sin^{2} \frac{7 π}{8} = 2$

Prove that: $\cos^{3} 2 x + 3 \cos 2 x = 4 (\cos^{6} x - \sin^{6} x)$

Prove that: $\cos^{6} A - \sin^{6} A = \cos 2 A (1 - \frac{1}{4} \sin^{2} 2 A)$

Prove that: $\cos 4 x - \cos 4 α = 8 (\cos x - \cos α) (\cos x + \cos α) (\cos x - \sin α) (\cos x + \sin α)$

Prove that: $\cot \frac{π}{8} = \sqrt{2} + 1$

If $\sin x = \frac{\sqrt{5}}{3}$ and x lies in IInd quadrant, find the values of $\cos \frac{x}{2}, \sin \frac{x}{2} and \tan \frac{x}{2}$ .

If $\cos x = \frac{4}{5}$ and x is acute, find tan 2x

If $tan x = \frac{b}{a}$ , then find the value of $\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}$ .

Prove that: $\cos \frac{π}{65} \cos \frac{2 π}{65} \cos \frac{4 π}{65} \cos \frac{8 π}{65} \cos \frac{16 π}{65} \cos \frac{32 π}{65} = \frac{1}{64}$

If $\sin α = \frac{4}{5} and \cos β = \frac{5}{13}$ , prove that $\cos \frac{α - β}{2} = \frac{8}{\sqrt{65}}$

Prove that: $\sin 5 x = 5 \sin x - 20 \sin^{3} x + 16 \sin^{5} x$

Prove that $\tan x + \tan (\frac{π}{3} + x) - \tan (\frac{π}{3} - x) = 3 \tan 3 x$

\sin 5 x = 5 \cos^{4} x \sin x - 10 \cos^{2} x \sin^{3} x + \sin^{5} x

Prove that : $\sin \frac{π}{5} \sin \frac{2 π}{5} \sin \frac{3 π}{5} \sin \frac{4 π}{5} = \frac{5}{16}$

If $\frac{π}{2} < x < \frac{3 π}{2}$ , then write the value of $\sqrt{\frac{1 + \cos 2 x}{2}}$

If $\frac{π}{2} < x < π$ , then write the value of $\frac{\sqrt{1 - \cos 2 x}}{1 + \cos 2 x}$ .

If $π < x < \frac{3 π}{2}$ , then write the value of $\sqrt{\frac{1 - \cos 2 x}{1 + \cos 2 x}}$ .

In a right angled triangle ABC, write the value of sin² A + Sin² B + Sin² C.

Write the value of $\cos \frac{π}{7} \cos \frac{2 π}{7} \cos \frac{4 π}{7} .$

The value of $\cos \frac{π}{65} \cos \frac{2 π}{65} \cos \frac{4 π}{65} \cos \frac{8 π}{65} \cos \frac{16 π}{65} \cos \frac{32 π}{65}$ is

If $\sin α + \sin β = a and \cos α - \cos β = b then \tan \frac{α - β}{2} =$

$\sin^{2} (\frac{π}{18}) + \sin^{2} (\frac{π}{9}) + \sin^{2} (\frac{7 π}{18}) + \sin^{2} (\frac{4 π}{9}) =$

$2 cos x - c o s 3 x - \cos 5 x - 16 \cos^{3} x \sin^{2} x$

If $(2^{n} + 1) x = π,$ then $2^{n} \cos x \cos 2 x \cos 2^{2} x . . . \cos 2^{n - 1} x = 1$

If $n = 1, 2, 3, . . ., then \cos α \cos 2 α \cos 4 α . . . \cos 2^{n - 1} α$ is equal to

The value of $\cos^{2} 48^{\circ} - \sin^{2} 12^{\circ}$ is ______.

The value of sin 20° sin 40° sin 60° sin 80° is ______.

If tanθ = $\frac{1}{2}$ and tanΦ = $\frac{1}{3}$ , then the value of θ + Φ is ______.

The value of sin50° – sin70° + sin10° is equal to ______.

If sinθ = $\frac{- 4}{5}$ and θ lies in the third quadrant then the value of $\cos \frac{θ}{2}$ is ______.

If tanA = $\frac{1 - \cos B}{\sin B}$ , then tan2A = ______.

8 Sin X 8 Cos X 2 Cos X 4 Cos X 8 is Equal to - Mathematics

Advertisements

Advertisements

प्रश्न

विकल्प

उत्तर

APPEARS IN

संबंधित प्रश्न

Select a course

8 Sin X 8 Cos X 2 Cos X 4 Cos X 8 is Equal to - Mathematics

Advertisements

Advertisements

प्रश्न

विकल्प

उत्तरShow Solution

APPEARS IN

संबंधित प्रश्न

Select a course

उत्तर