Advertisements
Advertisements
Question
Solve the following equation:
\[\cot x + \tan x = 2\]
Advertisements
Solution
\[ \Rightarrow \frac{1}{\tan x} + \tan x = 2\]
\[ \Rightarrow \tan^2 x + 1 = 2\tan x\]
\[ \Rightarrow \tan^2 x - 2\tan x + 1 = 0\]
\[ \Rightarrow \left( \tan x - 1 \right)^2 = 0\]
\[\Rightarrow \tan x = 1 = \tan\frac{\pi}{4}\]
\[ \Rightarrow x = n\pi + \frac{\pi}{4}, n \in Z \left( \tan\theta = \tan\alpha \Rightarrow \theta = n\pi + \alpha, n \in Z \right)\]
APPEARS IN
RELATED QUESTIONS
Find the general solution of cosec x = –2
Find the general solution for each of the following equations sec2 2x = 1– tan 2x
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
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 \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
Prove that:
\[\sec\left( \frac{3\pi}{2} - x \right)\sec\left( x - \frac{5\pi}{2} \right) + \tan\left( \frac{5\pi}{2} + x \right)\tan\left( x - \frac{3\pi}{2} \right) = - 1 .\]
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 tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
If tan θ + sec θ =ex, then cos θ equals
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:
Solve the following equation:
Solve the following equation:
Solve the following equation:
`cosec x = 1 + cot x`
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]
If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.
Write the number of points of intersection of the curves
Write the number of points of intersection of the curves
If \[\tan px - \tan qx = 0\], then the values of θ form a series in
If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ
Choose the correct alternative:
If tan 40° = λ, then `(tan 140^circ - tan 130^circ)/(1 + tan 140^circ * tan 130^circ)` =
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
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`
The minimum value of 3cosx + 4sinx + 8 is ______.
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
