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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 general solution of the equation cos 3x + cos x – cos 2x = 0


Find the general solution of the equation sin 2x + cos x = 0


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


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


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


Prove that:

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

 


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

 


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:

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

 


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


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

 

Which of the following is incorrect?


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

 

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

 

Which of the following is correct?


Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Solve the following equation:

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

Solve the following equation:

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

Solve the following equation:

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

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:

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

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


Solve the following equation:

\[\sqrt{3} \cos x + \sin x = 1\]


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\[2y = 1\] and \[y = \cos x, 0 \leq x \leq 2\pi\].
 

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


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