हिंदी

Write the Number of Points of Intersection of the Curves 2 Y = − 1 and Y = C O S E C X

Advertisements
Advertisements

प्रश्न

Write the number of points of intersection of the curves

\[2y = - 1 \text{ and }y = cosec x\]
योग
Advertisements

उत्तर

Given: 

2y = -1 and y= cosec x
Now,
2y = -1`=>`y = -`1/2`

\[cosecx = y\]

\[ \Rightarrow cosecx = - \frac{1}{2}\]

\[ \Rightarrow \frac{1}{\sin x} = - \frac{1}{2}\]

\[ \Rightarrow \sin x = - 2\]
The value of sine function lies between - 1 and 1. Therefore, the two curves will not intersect at any point.

Hence, the number of points of intersection of the curves is 0.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 11: Trigonometric equations - Exercise 11.2 [पृष्ठ २६]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 11 Trigonometric equations
Exercise 11.2 | Q 8 | पृष्ठ २६

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Find the general solution of the equation  sin x + sin 3x + sin 5x = 0


If \[x = \frac{2 \sin x}{1 + \cos x + \sin x}\], then prove that

\[\frac{1 - \cos x + \sin x}{1 + \sin x}\] is also equal to a.

If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that  \[ab + a - b + 1 = 0\]


Prove that: \[\tan\frac{11\pi}{3} - 2\sin\frac{4\pi}{6} - \frac{3}{4} {cosec}^2 \frac{\pi}{4} + 4 \cos^2 \frac{17\pi}{6} = \frac{3 - 4\sqrt{3}}{2}\]

 


Prove that

\[\frac{cosec(90^\circ + x) + \cot(450^\circ + x)}{cosec(90^\circ - x) + \tan(180^\circ - x)} + \frac{\tan(180^\circ + x) + \sec(180^\circ - x)}{\tan(360^\circ + x) - \sec( - x)} = 2\]

 


Prove that

\[\left\{ 1 + \cot x - \sec\left( \frac{\pi}{2} + x \right) \right\}\left\{ 1 + \cot x + \sec\left( \frac{\pi}{2} + x \right) \right\} = 2\cot x\]

 


In a ∆ABC, prove that:

\[\cos\left( \frac{A + B}{2} \right) = \sin\frac{C}{2}\]

 


Find x from the following equations:
\[cosec\left( \frac{\pi}{2} + \theta \right) + x \cos \theta \cot\left( \frac{\pi}{2} + \theta \right) = \sin\left( \frac{\pi}{2} + \theta \right)\]


If tan x + sec x = \[\sqrt{3}\], 0 < x < π, then x is equal to


If \[cosec x + \cot x = \frac{11}{2}\], then tan x =

 


If x sin 45° cos2 60° = \[\frac{\tan^2 60^\circ cosec30^\circ}{\sec45^\circ \cot^{2^\circ} 30^\circ}\], then x =

 

If sec x + tan x = k, cos x =


The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is

 

Find the general solution of the following equation:

\[\tan x = - \frac{1}{\sqrt{3}}\]

Find the general solution of the following equation:

\[\sin 2x = \frac{\sqrt{3}}{2}\]

Find the general solution of the following equation:

\[\tan mx + \cot nx = 0\]

Solve the following equation:

\[\cos 4 x = \cos 2 x\]

Solve the following equation:

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

Solve the following equation:

\[\sin 3x - \sin x = 4 \cos^2 x - 2\]

Solve the following equation:

\[\tan 3x + \tan x = 2\tan 2x\]

Solve the following equation:
\[\cot x + \tan x = 2\]

 


Solve the following equation:
 cosx + sin x = cos 2x + sin 2x

 


Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0


Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].


Write the number of points of intersection of the curves

\[2y = 1\] and \[y = \cos x, 0 \leq x \leq 2\pi\].
 

If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]

 


If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =


The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.


If \[\sqrt{3} \cos x + \sin x = \sqrt{2}\] , then general value of x is


The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval


Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`


Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

cos 2x = 1 − 3 sin x


Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0


Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.


If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.


If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.


Find the general solution of the equation sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×