Advertisements
Advertisements
प्रश्न
Solve the following equation:
sin x tan x – 1 = tan x – sin x
Advertisements
उत्तर
\[\sin x \tan x - 1 = \tan x - \sin x\]
\[ \Rightarrow \sin x \tan x - \tan x + \sin x - 1 = 0\]
\[ \Rightarrow \tan x\left( \sin x - 1 \right) + 1\left( \sin x - 1 \right) = 0\]
\[ \Rightarrow \left( \tan x + 1 \right)\left( \sin x - 1 \right) = 0\]
\[ \Rightarrow \left( \tan x + 1 \right) = 0\text{ or }\left( \sin x - 1 \right) = 0\]
\[ \Rightarrow \tan x = - 1\text{ or }\sin x = 1\]
\[ \Rightarrow \tan x = \tan\frac{3\pi}{4}\text{ or }\sin x = \sin\frac{\pi}{2}\]
\[ \Rightarrow x = n\pi + \frac{3\pi}{4}\text{ or }x = n\pi + \left( - 1 \right)^n \frac{\pi}{2}, n \in \mathbb{Z}\]
APPEARS IN
संबंधित प्रश्न
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
Prove that:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]
In a ∆ABC, prove that:
Find x from the following equations:
\[cosec\left( \frac{\pi}{2} + \theta \right) + x \cos \theta \cot\left( \frac{\pi}{2} + \theta \right) = \sin\left( \frac{\pi}{2} + \theta \right)\]
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 \[cosec x + \cot x = \frac{11}{2}\], then tan x =
Find the general solution of the following equation:
Find the general solution of the following equation:
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:
`cosec x = 1 + cot x`
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
Write the general solutions of tan2 2x = 1.
Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]
and cos 2x are in A.P.
Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].
If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of 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
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
If \[\sqrt{3} \cos x + \sin x = \sqrt{2}\] , then general value of x is
General solution of \[\tan 5 x = \cot 2 x\] is
If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are
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 for which solution lies in the interval 0° ≤ θ < 360°
2 sin2x + 1 = 3 sin x
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0
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.
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.
Find the general solution of the equation sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x
