\[2 \left( 1 - 2 \sin^2 7x \right) \sin 3x\] is equal to

\[\sin 17x - \sin 11x\] \[\text{ We have } , \] \[ 2\left( 1 - 2 \sin^2 7x \right) \sin 3x = 2\left( \cos 14x \right) \sin3x \] \[ \left[ \because \cos2x = 1 - 2 \sin^2 x \right]\] \[ = 2 \sin3x \cos 14x\] \[ = \sin 17x - \sin 11x\] \[ \left[ \because 2 sinA cosB = \sin\left( A + B \right) - \sin\left( A - B \right) \right] \] \[ \therefore 2\left( 1 - 2 \sin^2 7x \right) \sin 3x = \sin 17x - \sin 11x\]

2 ( 1 − 2 sin 2 7 x ) sin 3 x is equal to - Mathematics

प्रश्न

$2 (1 - 2 \sin^{2} 7 x) \sin 3 x$ is equal to

विकल्प

$\sin 17 x - \sin 11 x$
$\sin 11 x - \sin 17 x$
$\cos 17 x - \cos 11 x$
$\cos 17 x + \cos 11 x$

MCQ

उत्तर

$\sin 17 x - \sin 11 x$

$We have,$

$2 (1 - 2 \sin^{2} 7 x) \sin 3 x = 2 (\cos 14 x) \sin 3 x$

$[∵ \cos 2 x = 1 - 2 \sin^{2} x]$

$= 2 \sin 3 x \cos 14 x$

$= \sin 17 x - \sin 11 x$

$[∵ 2 s i n A c o s B = \sin (A + B) - \sin (A - B)]$

$∴ 2 (1 - 2 \sin^{2} 7 x) \sin 3 x = \sin 17 x - \sin 11 x$

shaalaa.com

Values of Trigonometric Functions at Multiples and Submultiples of an Angle

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 24 Q 23 Q 25

अध्याय 9: Values of Trigonometric function at multiples and submultiples of an angle - Exercise 9.5 [पृष्ठ ४४]

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 24 | पृष्ठ ४४

संबंधित प्रश्न

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

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

Prove that: $\frac{\cos 2 x}{1 + \sin 2 x} = \tan (\frac{π}{4} - x)$

Prove that: $\tan (\frac{π}{4} + x) + \tan (\frac{π}{4} - x) = 2 \sec 2 x$

Prove that: $\cot^{2} x - \tan^{2} x = 4 \cot 2 x cosec 2 x$

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

If $\sec (x + α) + \sec (x - α) = 2 \sec x$ , prove that $\cos x = \pm \sqrt{2} \cos \frac{α}{2}$

If $\cos α + \cos β = 0 = \sin α + \sin β$ , then prove that $\cos 2 α + \cos 2 β = - 2 \cos (α + β)$ .

Prove that: $4 (\cos^{3} 10 ° + \sin^{3} 20 °) = 3 (\cos 10 ° + \sin 2 °)$

Prove that: $\cos^{3} x \sin 3 x + \sin^{3} x \cos 3 x = \frac{3}{4} \sin 4 x$

$\cot x + \cot (\frac{π}{3} + x) + \cot (\frac{2 π}{3} + x) = 3 \cot 3 x$

Prove that: $\cos \frac{π}{15} \cos \frac{2 π}{15} \cos \frac{4 π}{15} \cos \frac{7 π}{15} = \frac{1}{16}$

Prove that: $\cos 36 ° \cos 42 ° \cos 60 ° \cos 78 ° = \frac{1}{16}$

Prove that: $\cos \frac{π}{15} \cos \frac{2 π}{15} \cos \frac{3 π}{15} \cos \frac{4 π}{15} \cos \frac{5 π}{15} \cos \frac{6 π}{15} \cos \frac{7 π}{15} = \frac{1}{128}$

If $\frac{π}{2} < x < π,$ the write the value of $\sqrt{2 + \sqrt{2 + 2 \cos 2 x}}$ in the simplest form.

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

If $sin x + cos x = a$ , find the value of $| sin x - cos x |$ .

\frac{\sec 8 A - 1}{\sec 4 A - 1} =

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

The value of $2 \tan \frac{π}{10} + 3 \sec \frac{π}{10} - 4 \cos \frac{π}{10}$ is

If in a $∆ A B C, \tan A + \tan B + \tan C = 0$ , then

\cot A \cot B \cot C =

If $\cos x = \frac{1}{2} (a + \frac{1}{a}),$ and $\cos 3 x = λ (a^{3} + \frac{1}{a^{3}})$ then $λ =$

If $\tan α = \frac{1 - \cos β}{\sin β}$ , then

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

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

$\frac{\sin 3 x}{1 + 2 \cos 2 x}$ is equal to

If α and β are acute angles satisfying $\cos 2 α = \frac{3 \cos 2 β - 1}{3 - \cos 2 β}$ , then tan α =

The value of $\cos (36 ° - A) \cos (36 ° + A) + \cos (54 ° - A) \cos (54 ° + A)$ is

The value of $\tan x + \tan (\frac{π}{3} + x) + \tan (\frac{2 π}{3} + x)$ is

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

If A = cos²θ + sin⁴θ for all values of θ, then prove that $\frac{3}{4}$ ≤ A ≤ 1.

If acos2θ + bsin2θ = c has α and β as its roots, then prove that tanα + tanβ = $\frac{2 b}{a + c}$ .

$[Hint: Use the identities \cos 2 θ = \frac{1 - \tan^{2} θ}{1 + \tan^{2} θ} and \sin 2 θ = \frac{2 \tan θ}{1 + \tan^{2} θ}]$ .

The value of $\sin \frac{π}{10} \sin \frac{13 π}{10}$ is ______.

$[Hint: Use {\sin 18}^{\circ} = \frac{\sqrt{5} - 1}{4} and {\cos 36}^{\circ} = \frac{\sqrt{5} + 1}{4}]$

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

2 ( 1 − 2 sin 2 7 x ) sin 3 x is equal to - Mathematics

Advertisements

Advertisements

प्रश्न

विकल्प

उत्तर

APPEARS IN

संबंधित प्रश्न

Select a course

2 ( 1 − 2 sin 2 7 x ) sin 3 x is equal to - Mathematics

Advertisements

Advertisements

प्रश्न

विकल्प

उत्तरShow Solution

APPEARS IN

संबंधित प्रश्न

Select a course

उत्तर