Advertisements
Advertisements
प्रश्न
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
पर्याय
- \[\frac{21}{22}\]
- \[\frac{15}{16}\]
- \[\frac{44}{117}\]
- \[\frac{117}{43}\]
उत्तर
We have:
\[ cosec x + \cot x = \frac{11}{2} \left( 1 \right)\]
\[ \Rightarrow \frac{1}{cosec x + \cot x} = \frac{2}{11}\]
\[ \Rightarrow \frac{{cosec}^2 x - \cot^2 x}{cosec x + \cot x} = \frac{2}{11}$\]
\[ \Rightarrow \frac{\left( cosec x + \cot x \right)\left( cosec x - \cot x \right)}{\left( cosec x + \cot x \right)} = \frac{2}{11}\]
\[ \therefore cosecx-\cot x = \frac{2}{11} \left( 2 \right)\]
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 \[\cot x \left( 1 + \sin x \right) = 4 m \text{ and }\cot x \left( 1 - \sin x \right) = 4 n,\] \[\left( m^2 + n^2 \right)^2 = mn\]
If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
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:
\[\sin \frac{13\pi}{3}\sin\frac{2\pi}{3} + \cos\frac{4\pi}{3}\sin\frac{13\pi}{6} = \frac{1}{2}\]
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
sin6 A + cos6 A + 3 sin2 A cos2 A =
If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]
sin2 π/18 + sin2 π/9 + sin2 7π/18 + sin2 4π/9 =
If tan θ + sec θ =ex, then cos θ equals
Which of the following is incorrect?
The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] 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:
Solve the following equation:
Solve the following equation:
\[\sin x + \cos x = \sqrt{2}\]
Solve the following equation:
`cosec x = 1 + cot x`
Solve the following equation:
\[\cot x + \tan x = 2\]
Solve the following equation:
\[2 \sin^2 x = 3\cos x, 0 \leq x \leq 2\pi\]
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
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 solution set of the equation
If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
Solve the following equations:
sin 5x − sin x = cos 3
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
Choose the correct alternative:
`(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x)` is equal to
Solve the equation sin θ + sin 3θ + sin 5θ = 0
Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.
