English

Find the General Solution for Each of the Following Equations Sec2 2x = 1– Tan 2x - Mathematics

Advertisements
Advertisements

Question

Find the general solution for each of the following equations sec2 2x = 1– tan 2x

Advertisements

Solution

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Trigonometric Functions - Exercise 3.4 [Page 78]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 3 Trigonometric Functions
Exercise 3.4 | Q 8 | Page 78

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


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


Prove the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]


Prove that:  tan 225° cot 405° + tan 765° cot 675° = 0


Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]


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

Prove that:

\[3\sin\frac{\pi}{6}\sec\frac{\pi}{3} - 4\sin\frac{5\pi}{6}\cot\frac{\pi}{4} = 1\]

 


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

 


In a ∆ABC, prove that:
cos (A + B) + cos C = 0


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


Prove that:

\[\sin\frac{10\pi}{3}\cos\frac{13\pi}{6} + \cos\frac{8\pi}{3}\sin\frac{5\pi}{6} = - 1\]

If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to

 


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

 

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:

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

Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Solve the following equation:

\[\tan^2 x + \left( 1 - \sqrt{3} \right) \tan x - \sqrt{3} = 0\]

Solve the following equation:

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

Solve the following equation:

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

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

 


Solve the following equation:
4sinx cosx + 2 sin x + 2 cosx + 1 = 0 


Solve the following equation:
 sin x tan x – 1 = tan x – sin x

 


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.


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


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

 


If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are


Solve the following equations:
sin 5x − sin x = cos 3


Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval


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


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×