English

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

Advertisements
Advertisements

Question

Find the general solution of the following equation:

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

Solution

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
  Is there an error in this question or solution?
Chapter 11: Trigonometric equations - Exercise 11.1 [Page 21]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 11 Trigonometric equations
Exercise 11.1 | Q 1.4 | Page 21

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


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


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 \[\sin x + \cos x = m\], then prove that \[\sin^6 x + \cos^6 x = \frac{4 - 3 \left( m^2 - 1 \right)^2}{4}\], where \[m^2 \leq 2\]


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: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 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:

\[\tan\frac{5\pi}{4}\cot\frac{9\pi}{4} + \tan\frac{17\pi}{4}\cot\frac{15\pi}{4} = 0\]

 


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


If tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is

 

\[\sec^2 x = \frac{4xy}{(x + y )^2}\] is true if and only if

 


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

 

If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to


If tan θ + sec θ =ex, then cos θ equals


If sec x + tan x = k, cos x =


Find the general solution of the following equation:

\[\sqrt{3} \sec x = 2\]

Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Solve the following equation:

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

Solve the following equation:

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

Solve the following equation:

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

Solve the following equation:

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

Solve the following equation:

\[\sin x + \cos x = 1\]

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:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0


If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.


Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]


Write the solution set of the equation 

\[\left( 2 \cos x + 1 \right) \left( 4 \cos x + 5 \right) = 0\] in the interval [0, 2π].

If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.


The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is


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


The number of values of x in the interval [0, 5 π] satisfying the equation \[3 \sin^2 x - 7 \sin x + 2 = 0\] is


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


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


Solve the following equations:
2cos 2x – 7 cos x + 3 = 0


Choose the correct alternative:
If tan α and tan β are the roots of x2 + ax + b = 0 then `(sin(alpha + beta))/(sin alpha sin beta)` is equal to


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×