मराठी

Write the General Solutions of Tan2 2x = 1.

Advertisements
Advertisements

प्रश्न

Write the general solutions of tan2 2x = 1.

 
बेरीज
Advertisements

उत्तर

Given: 
\[\tan^2 2x = 1\]
\[ \Rightarrow \tan 2x = \tan \frac{\pi}{4}\]
\[ \Rightarrow 2x = n\pi + \frac{\pi}{4}\]
\[ \Rightarrow x = \frac{n\pi}{2} + \frac{\pi}{8}, n \in Z\]
Hence, the general solution of the equation is 
\[\frac{n\pi}{2} + \frac{\pi}{8}, n \in Z .\]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Trigonometric equations - Exercise 11.2 [पृष्ठ २६]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 11 Trigonometric equations
Exercise 11.2 | Q 3 | पृष्ठ २६

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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 \[T_n = \sin^n x + \cos^n x\], prove that \[\frac{T_3 - T_5}{T_1} = \frac{T_5 - T_7}{T_3}\]

 


In a ∆ABC, prove that:

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

 


In a ∆ABC, prove that:

\[\tan\frac{A + B}{2} = \cot\frac{C}{2}\]

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


Prove that:

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

 


If \[\frac{\pi}{2} < x < \pi, \text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}}\] is equal to


If \[\frac{3\pi}{4} < \alpha < \pi, \text{ then }\sqrt{2\cot \alpha + \frac{1}{\sin^2 \alpha}}\] is equal to


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

 


sin2 π/18 + sin2 π/9 + sin2 7π/18 + sin2 4π/9 =


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

 

Find the general solution of the following equation:

\[cosec x = - \sqrt{2}\]

Find the general solution of the following equation:

\[\sin 2x = \cos 3x\]

Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Solve the following equation:
\[\sin^2 x - \cos x = \frac{1}{4}\]


Solve the following equation:

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

Solve the following equation:

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

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:

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

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:
 sin x tan x – 1 = tan x – sin x

 


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


If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).


The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]


The smallest positive angle which satisfies the equation ​

\[2 \sin^2 x + \sqrt{3} \cos x + 1 = 0\] is

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

 


A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is

 

In (0, π), the number of solutions of the equation ​ \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is 


Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`


Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ


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


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×