Advertisements
Advertisements
प्रश्न
विकल्प
cosec x + cot x
cosec x − cot x
−cosec x + cot x
−cosec x − cot x
Advertisements
उत्तर
−cosec x − cot x
\[\sqrt{\frac{1 + \cos x}{1 - \cos x}} \]
\[ = \sqrt{\frac{\left( 1 + \cos x \right)\left( 1 + \cos x \right)}{\left( 1 - \cos x \right)\left( 1 + \cos x \right)}}\]
\[ = \sqrt{\frac{\left( 1 + \cos x \right)^2}{1 - \cos^2 x}}\]
\[ = \sqrt{\frac{\left( 1 + \cos x \right)^2}{\sin^2 x}}\]
\[ = \frac{\left( 1 + \cos x \right)}{- \sin x} \left[\text{ as, }\pi < x < 2\pi,\text{ so }\sin x\text{ will be negative }\right]\]
\[ = - \left( cosec x + \cot x \right) \]
\[ = - cosec x - \cot x\]
APPEARS IN
संबंधित प्रश्न
Find the principal and general solutions of the equation sec x = 2
Find the general solution for each of the following equations sec2 2x = 1– tan 2x
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: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]
Prove that
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 \[\frac{3\pi}{4} < \alpha < \pi, \text{ then }\sqrt{2\cot \alpha + \frac{1}{\sin^2 \alpha}}\] is equal to
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[\cot x + \tan x = 2\]
Solve the following equation:
cosx + sin x = cos 2x + sin 2x
Solve the following equation:
sin x tan x – 1 = tan x – sin x
Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].
Write the set of values of a for which the equation
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]
and cos 2x are in A.P.
If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.
If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
In (0, π), the number of solutions of the equation \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is
General solution of \[\tan 5 x = \cot 2 x\] is
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 θ + cos θ = `sqrt(2)`
Solve the following equations:
cot θ + cosec θ = `sqrt(3)`
Solve the following equations:
2cos 2x – 7 cos x + 3 = 0
Solve the equation sin θ + sin 3θ + sin 5θ = 0
If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0
