हिंदी

Find the General Solution of the Following Equation: Sec X = √ 2 - Mathematics

Advertisements
Advertisements

प्रश्न

Find the general solution of the following equation:

\[\sec x = \sqrt{2}\]
योग
Advertisements

उत्तर

We have:
\[\sec x = \sqrt{2}\] (or) 

\[\cos x = \frac{1}{\sqrt{2}}\]
The value of x satisfying \[\cos x = \frac{1}{\sqrt{2}}\] is \[\frac{\pi}{4}\]
∴ \[\cos x = \frac{1}{\sqrt{2}}\]
⇒ \[\cos x = \cos \frac{\pi}{4}\]
⇒ \[x = 2n\pi \pm \frac{\pi}{4}\],
\[n \in Z\]
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 11: Trigonometric equations - Exercise 11.1 [पृष्ठ २१]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 11 Trigonometric equations
Exercise 11.1 | Q 1.4 | पृष्ठ २१

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Find the principal and general solutions of the equation  `cot x = -sqrt3`


Find the general solution of the equation cos 4 x = cos 2 x


Find the general solution of the equation cos 3x + cos x – cos 2x = 0


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


If \[cosec x - \sin x = a^3 , \sec x - \cos x = b^3\], then prove that \[a^2 b^2 \left( a^2 + b^2 \right) = 1\]


If \[\cot x \left( 1 + \sin x \right) = 4 m \text{ and }\cot x \left( 1 - \sin x \right) = 4 n,\] \[\left( m^2 + n^2 \right)^2 = mn\]


Prove that:

\[\sin\frac{8\pi}{3}\cos\frac{23\pi}{6} + \cos\frac{13\pi}{3}\sin\frac{35\pi}{6} = \frac{1}{2}\]

 


Prove that cos 570° sin 510° + sin (−330°) cos (−390°) = 0

In a ∆A, B, C, D be the angles of a cyclic quadrilateral, taken in order, prove that cos(180° − A) + cos (180° + B) + cos (180° + C) − sin (90° + D) = 0


Prove that:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]


sin6 A + cos6 A + 3 sin2 A cos2 A =


If x is an acute angle and \[\tan x = \frac{1}{\sqrt{7}}\], then the value of \[\frac{{cosec}^2 x - \sec^2 x}{{cosec}^2 x + \sec^2 x}\] is


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

 

The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] is

 

Find the general solution of the following equation:

\[\cos 3x = \frac{1}{2}\]

Find the general solution of the following equation:

\[\tan x + \cot 2x = 0\]

Find the general solution of the following equation:

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

Find the general solution of the following equation:

\[\sin x = \tan x\]

Solve the following equation:

\[4 \sin^2 x - 8 \cos x + 1 = 0\]

Solve the following equation:

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

Solve the following equation:

\[\sqrt{3} \cos x + \sin x = 1\]


Solve the following equation:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]


Solve the following equation:
\[\sin x - 3\sin2x + \sin3x = \cos x - 3\cos2x + \cos3x\]


Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2


Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].


The smallest value of x satisfying the equation

\[\sqrt{3} \left( \cot x + \tan x \right) = 4\] is 

If \[\tan px - \tan qx = 0\], then the values of θ form a series in

 


If \[4 \sin^2 x = 1\], then the values of x are

 


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

2 sin2x + 1 = 3 sin x


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

cos 2x = 1 − 3 sin x


Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ


Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1


Choose the correct alternative:
If tan 40° = λ, then `(tan 140^circ - tan 130^circ)/(1 + tan 140^circ *  tan 130^circ)` =


Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to


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


The minimum value of 3cosx + 4sinx + 8 is ______.


Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.


In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×