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 for each of the following equations sec2 2x = 1– tan 2x
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 \[\frac{T_3 - T_5}{T_1} = \frac{T_5 - T_7}{T_3}\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[2 T_6 - 3 T_4 + 1 = 0\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]
Prove that
In a ∆ABC, prove that:
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:
\[\tan 4\pi - \cos\frac{3\pi}{2} - \sin\frac{5\pi}{6}\cos\frac{2\pi}{3} = \frac{1}{4}\]
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 tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to
If \[0 < x < \frac{\pi}{2}\], and if \[\frac{y + 1}{1 - y} = \sqrt{\frac{1 + \sin x}{1 - \sin x}}\], then y is equal to
If \[cosec x + \cot x = \frac{11}{2}\], then tan 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:
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:
Solve the following equation:
\[\cot x + \tan x = 2\]
Solve the following equation:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]
Solve the following equation:
4sinx cosx + 2 sin x + 2 cosx + 1 = 0
If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]
If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
If \[\cot x - \tan x = \sec x\], then, x is equal to
Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0
Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ
Solve the following equations:
2cos 2x – 7 cos x + 3 = 0
If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
