मराठी

Find the General Solution of the Following Equation: Sin X = Tan X

Advertisements
Advertisements

प्रश्न

Find the general solution of the following equation:

\[\sin x = \tan x\]
बेरीज
Advertisements

उत्तर

We have:

\[\sin x = \tan x\]
\[\Rightarrow \sin x - \tan x = 0\]
\[ \Rightarrow \sin x - \frac{\sin x}{\cos x} = 0\]
\[ \Rightarrow \sin x \left( 1 - \frac{1}{\cos x} \right) = 0\]
\[ \Rightarrow \sin x (\cos x - 1) = 0\]
\[\Rightarrow \sin x = 0\] or
\[\cos x - 1 = 0\]
Now,  
\[\sin x = 0 \Rightarrow x = n\pi, n \in Z\]

\[\cos x - 1 = 0 \]

\[ \Rightarrow \cos x = 1 \]

\[ \Rightarrow \cos x = \cos0 \]

\[ \Rightarrow x = 2m\pi, m \in Z\]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Trigonometric equations - Exercise 11.1 [पृष्ठ २१]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 11 Trigonometric equations
Exercise 11.1 | Q 2.11 | पृष्ठ २१

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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

 


Prove that:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]

 


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 (A + B) + cos C = 0


If \[0 < x < \frac{\pi}{2}\], and if \[\frac{y + 1}{1 - y} = \sqrt{\frac{1 + \sin x}{1 - \sin x}}\], then y is equal to


If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]

 

If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then


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

 

Which of the following is correct?


Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Find the general solution of the following equation:

\[\sin 9x = \sin x\]

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:

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

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

 


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

 


Solve the following equation:
3tanx + cot x = 5 cosec x


Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]


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


Write the set of values of a for which the equation

\[\sqrt{3} \sin x - \cos x = a\] has no solution.

Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]

 and cos 2x are in A.P.


Write the number of points of intersection of the curves

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

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


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


Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`


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


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


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


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


Solve the equation sin θ + sin 3θ + sin 5θ = 0


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×