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Find the Principal and General Solutions of the Equation `Tan X = Sqrt3` - Mathematics

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

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अध्याय 3: Trigonometric Functions - Exercise 3.4 [पृष्ठ ७८]

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एनसीईआरटी Mathematics [English] Class 11
अध्याय 3 Trigonometric Functions
Exercise 3.4 | Q 1 | पृष्ठ ७८

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संबंधित प्रश्न

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


Find the general solution of cosec x = –2


If \[\tan x = \frac{a}{b},\] show that

\[\frac{a \sin x - b \cos x}{a \sin x + b \cos x} = \frac{a^2 - b^2}{a^2 + b^2}\]

If \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]


Prove that: \[\tan\frac{11\pi}{3} - 2\sin\frac{4\pi}{6} - \frac{3}{4} {cosec}^2 \frac{\pi}{4} + 4 \cos^2 \frac{17\pi}{6} = \frac{3 - 4\sqrt{3}}{2}\]

 


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

\[\frac{cosec(90^\circ + x) + \cot(450^\circ + x)}{cosec(90^\circ - x) + \tan(180^\circ - x)} + \frac{\tan(180^\circ + x) + \sec(180^\circ - x)}{\tan(360^\circ + x) - \sec( - x)} = 2\]

 


Find x from the following equations:
\[x \cot\left( \frac{\pi}{2} + \theta \right) + \tan\left( \frac{\pi}{2} + \theta \right)\sin \theta + cosec\left( \frac{\pi}{2} + \theta \right) = 0\]


Prove that:
\[\tan 4\pi - \cos\frac{3\pi}{2} - \sin\frac{5\pi}{6}\cos\frac{2\pi}{3} = \frac{1}{4}\]


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 = \[x - \frac{1}{4x}\], then sec x − tan x is equal to


If sec \[x = x + \frac{1}{4x}\], then sec x + tan x = 

 

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


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


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


If tan A + cot A = 4, then tan4 A + cot4 A is equal to


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

 

If sec x + tan x = k, cos x =


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

 

The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is

 

Find the general solution of the following equation:

\[\sin x = \frac{1}{2}\]

Find the general solution of the following equation:

\[\cos x = - \frac{\sqrt{3}}{2}\]

Find the general solution of the following equation:

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

Solve the following equation:

\[2 \cos^2 x - 5 \cos x + 2 = 0\]

Solve the following equation:

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

Solve the following equation:

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

Solve the following equation:

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

Solve the following equation:

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

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


Solve the following equation:

`cosec  x = 1 + cot x`


Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].


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


If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.


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


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


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

2 sin2x + 1 = 3 sin x


Choose the correct alternative:
If cos pθ + cos qθ = 0 and if p ≠ q, then θ is equal to (n is any integer)


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


If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2 


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