Advertisements
Advertisements
प्रश्न
If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to
विकल्प
sec x − tan x
sec x + tan x
tan x − sec x
none of these
Advertisements
उत्तर
tan x − sec x
\[\sqrt{\frac{1 - \sin x}{1 + \sin x}} \]
\[ = \sqrt{\frac{\left( 1 - \sin x \right)\left( 1 - \sin x \right)}{\left( 1 + \sin x \right)\left( 1 - \sin x \right)}}\]
\[ = \sqrt{\frac{\left( 1 - \sin x \right)^2}{1 - \sin^2 x}}\]
\[ = \sqrt{\frac{\left( 1 - \sin x \right)^2}{\cos^2 x}}\]
\[ = \frac{\left( 1 - \sin x \right)}{- cos x} \left[\text{ as,} \frac{\pi}{2} < x < \frac{3\pi}{2},\text{ so }\cos\theta\text{ will be negative }\right]\]
\[ = - \left( sec x - \tan x \right) \]
\[ = - sec x + \tan x\]
APPEARS IN
संबंधित प्रश्न
Find the general solution of the equation cos 4 x = cos 2 x
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
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 \[\sin x + \cos x = m\], 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 \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]
Prove that
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:
\[x \cot\left( \frac{\pi}{2} + \theta \right) + \tan\left( \frac{\pi}{2} + \theta \right)\sin \theta + cosec\left( \frac{\pi}{2} + \theta \right) = 0\]
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then x2 + y2 + z2 is independent of
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
Which of the following is correct?
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:
\[\sin x + \cos x = \sqrt{2}\]
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:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]
Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]
Write the set of values of a for which the equation
Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]
and cos 2x are in A.P.
If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
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 \[\sin^2 x - \cos x = \frac{1}{4}\]
The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval
If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
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 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
