Advertisements
Advertisements
प्रश्न
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
पर्याय
- \[\frac{21}{22}\]
- \[\frac{15}{16}\]
- \[\frac{44}{117}\]
- \[\frac{117}{44}\]
Advertisements
उत्तर
We have:
\[ cosec x + \cot x = \frac{11}{2} \left( 1 \right)\]
\[ \Rightarrow \frac{1}{cosecx + \cot x} = \frac{2}{11}\]
\[ \Rightarrow \frac{{cosec}^2 x - \cot^2 x}{cosecx + \cot x} = \frac{2}{11}\]
\[ \Rightarrow \frac{\left( cosec x + \cot x \right)\left( cosec x - \cot x \right)}{\left( cosec x + \cot x \right)} = \frac{2}{11}\]
\[ \therefore cosec A-\cot x = \frac{2}{11} \left( 2 \right)\]
Subtracting ( 2 ) from ( 1 ):
\[2\cot x = \frac{11}{2} - \frac{2}{11}\]
\[ \Rightarrow 2\cot x = \frac{121 - 4}{22}\]
\[ \Rightarrow 2\cot x = \frac{117}{22}\]
\[ \Rightarrow \cot x = \frac{117}{44}\]
\[ \Rightarrow \frac{1}{\tan x} = \frac{117}{44}\]
\[ \Rightarrow \tan x = \frac{44}{117}\]
APPEARS IN
संबंधित प्रश्न
Find the general solution of the equation sin 2x + cos x = 0
Find the general solution of the equation sin x + sin 3x + sin 5x = 0
If \[\tan x = \frac{b}{a}\] , then find the values of \[\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}\].
If \[cosec x - \sin x = a^3 , \sec x - \cos x = b^3\], then prove that \[a^2 b^2 \left( a^2 + b^2 \right) = 1\]
Prove that:
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 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:
\[\sec\left( \frac{3\pi}{2} - x \right)\sec\left( x - \frac{5\pi}{2} \right) + \tan\left( \frac{5\pi}{2} + x \right)\tan\left( x - \frac{3\pi}{2} \right) = - 1 .\]
In a ∆ABC, prove that:
Find x from the following equations:
\[cosec\left( \frac{\pi}{2} + \theta \right) + x \cos \theta \cot\left( \frac{\pi}{2} + \theta \right) = \sin\left( \frac{\pi}{2} + \theta \right)\]
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 =
sin6 A + cos6 A + 3 sin2 A cos2 A =
If x sin 45° cos2 60° = \[\frac{\tan^2 60^\circ cosec30^\circ}{\sec45^\circ \cot^{2^\circ} 30^\circ}\], then x =
The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is
Find the general solution of the following equation:
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[\sin x - 3\sin2x + \sin3x = \cos x - 3\cos2x + \cos3x\]
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
Write the general solutions of tan2 2x = 1.
Write the set of values of a for which the equation
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.
The smallest value of x satisfying the equation
A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is
The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 cos2x + 1 = – 3 cos x
Solve the following equations:
2 cos2θ + 3 sin θ – 3 = θ
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Choose the correct alternative:
If tan 40° = λ, then `(tan 140^circ - tan 130^circ)/(1 + tan 140^circ * tan 130^circ)` =
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
