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Find the Principal and General Solutions of the Equation Sec X = 2 - Mathematics

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प्रश्न

Find the principal and general solutions of the equation sec x = 2

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उत्तर

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

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एनसीईआरटी Mathematics [English] Class 11
पाठ 3 Trigonometric Functions
Exercise 3.4 | Q 2 | पृष्ठ ७८

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the general solution of cosec x = –2


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 \[\sin x + \cos x = m\], then prove that \[\sin^6 x + \cos^6 x = \frac{4 - 3 \left( m^2 - 1 \right)^2}{4}\], where \[m^2 \leq 2\]


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:

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

 


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

 


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

 

If \[cosec x + \cot x = \frac{11}{2}\], then tan x =

 


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


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


Which of the following is correct?


Find the general solution of the following equation:

\[\tan 3x = \cot x\]

Find the general solution of the following equation:

\[\tan 2x \tan x = 1\]

Find the general solution of the following equation:

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

Find the general solution of the following equation:

\[\tan px = \cot qx\]

 


Solve the following equation:

\[4 \sin^2 x - 8 \cos x + 1 = 0\]

Solve the following equation:

\[3 \cos^2 x - 2\sqrt{3} \sin x \cos x - 3 \sin^2 x = 0\]

Solve the following equation:

\[\cos 4 x = \cos 2 x\]

Solve the following equation:

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

Solve the following equation:

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

Solve the following equation:

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


Solve the following equation:
\[2 \sin^2 x = 3\cos x, 0 \leq x \leq 2\pi\]


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

 


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


If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.

 

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


The smallest value of x satisfying the equation

\[\sqrt{3} \left( \cot x + \tan x \right) = 4\] is 

The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is


A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval


The smallest positive angle which satisfies the equation ​

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

The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.


Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`


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

cos 2x = 1 − 3 sin x


Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`


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


Find the general solution of the equation sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x


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


In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.


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