Advertisements
Advertisements
प्रश्न
If sec \[x = x + \frac{1}{4x}\], then sec x + tan x =
पर्याय
- \[x, \frac{1}{x}\]
- \[2x, \frac{1}{2x}\]
- \[- 2x, \frac{1}{2x}\]
- \[- \frac{1}{x}, x\]
Advertisements
उत्तर
We have,
\[secx = x + \frac{1}{4x}\]
\[ \Rightarrow se c^2 x = = x^2 + \frac{1}{16 x^2} + \frac{1}{2}\]
\[ \Rightarrow 1 + \tan^2 x = 1 + x^2 + \frac{1}{16 x^2} - \frac{1}{2}\]
\[ \Rightarrow \tan^2 x = x^2 + \frac{1}{16 x^2} - \frac{1}{2}\]
\[ \Rightarrow \tan^2 x = \left( x - \frac{1}{4x} \right)^2 \]
\[ \therefore \tan x = \pm \left( x - \frac{1}{4x} \right)\]
\[ \Rightarrow sec x - \tan x = \left( x + \frac{1}{4x} \right) - \left( x - \frac{1}{4x} \right) or \left( x + \frac{1}{4x} \right) - \left[ - \left( x - \frac{1}{4x} \right) \right]\]
\[ = \frac{1}{2x}\text{ or }2x\]
APPEARS IN
संबंधित प्रश्न
Find the principal and general solutions of the equation `cot x = -sqrt3`
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 \[2 T_6 - 3 T_4 + 1 = 0\]
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:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]
Prove that:
\[\sec\left( \frac{3\pi}{2} - x \right)\sec\left( x - \frac{5\pi}{2} \right) + \tan\left( \frac{5\pi}{2} + x \right)\tan\left( x - \frac{3\pi}{2} \right) = - 1 .\]
Find x from the following equations:
\[cosec\left( \frac{\pi}{2} + \theta \right) + x \cos \theta \cot\left( \frac{\pi}{2} + \theta \right) = \sin\left( \frac{\pi}{2} + \theta \right)\]
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:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]
Prove that:
If tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to
If x is an acute angle and \[\tan x = \frac{1}{\sqrt{7}}\], then the value of \[\frac{{cosec}^2 x - \sec^2 x}{{cosec}^2 x + \sec^2 x}\] is
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
If tan A + cot A = 4, then tan4 A + cot4 A is equal to
If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to
If sec x + tan x = k, cos x =
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:
\[\sin^2 x - \cos x = \frac{1}{4}\]
Solve the following equation:
4sinx cosx + 2 sin x + 2 cosx + 1 = 0
Solve the following equation:
3tanx + cot x = 5 cosec x
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is
In (0, π), the number of solutions of the equation \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is
Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`
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)`
Solve the following equations:
2cos 2x – 7 cos x + 3 = 0
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 sin α + cos α = b, then sin 2α is equal to
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`
Find the general solution of the equation sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x
