Advertisements
Advertisements
प्रश्न
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
विकल्प
- \[\frac{21}{22}\]
- \[\frac{15}{16}\]
- \[\frac{44}{117}\]
- \[\frac{117}{44}\]
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
If \[x = \frac{2 \sin x}{1 + \cos x + \sin x}\], then prove that
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 \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
Prove that
Prove that
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:
Prove that:
\[\tan 4\pi - \cos\frac{3\pi}{2} - \sin\frac{5\pi}{6}\cos\frac{2\pi}{3} = \frac{1}{4}\]
If tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is
If tan A + cot A = 4, then tan4 A + cot4 A is equal to
Which of the following is correct?
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:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[\sin x + \cos x = \sqrt{2}\]
Solve the following equation:
\[\sqrt{3} \cos x + \sin x = 1\]
Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]
If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.
Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]
and cos 2x are in A.P.
Write the number of points of intersection of the curves
The smallest positive angle which satisfies the equation
If \[4 \sin^2 x = 1\], then the values of x are
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 \[\sin^2 x - \cos x = \frac{1}{4}\]
General solution of \[\tan 5 x = \cot 2 x\] is
If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are
The number of values of x in the interval [0, 5 π] satisfying the equation \[3 \sin^2 x - 7 \sin x + 2 = 0\] is
Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
Solve the following equations:
2cos 2x – 7 cos x + 3 = 0
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 tan α and tan β are the roots of x2 + ax + b = 0 then `(sin(alpha + beta))/(sin alpha sin beta)` is equal to
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
