Advertisements
Advertisements
Question
Find the principal and general solutions of the equation `tan x = sqrt3`
Solution
APPEARS IN
RELATED QUESTIONS
If \[\tan x = \frac{b}{a}\] , then find the values of \[\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}\].
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 \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
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 \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to
If tan x + sec x = \[\sqrt{3}\], 0 < x < π, then x is equal to
If \[\frac{3\pi}{4} < \alpha < \pi, \text{ then }\sqrt{2\cot \alpha + \frac{1}{\sin^2 \alpha}}\] is equal to
If x is an acute angle and \[\tan x = \frac{1}{\sqrt{7}}\], then the value of \[\frac{{cosec}^2 x - \sec^2 x}{{cosec}^2 x + \sec^2 x}\] is
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
If tan A + cot A = 4, then tan4 A + cot4 A is equal to
Which of the following is incorrect?
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:
\[\cot x + \tan x = 2\]
Solve the following equation:
3tanx + cot x = 5 cosec x
If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.
Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].
Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
Write the number of points of intersection of the curves
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 smallest positive angle which satisfies the equation
If \[4 \sin^2 x = 1\], then the values of x are
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 sin2x + 1 = 3 sin x
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
cos 2x = 1 − 3 sin x
Solve the following equations:
sin 5x − sin x = cos 3
Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ
Solve the following equations:
sin θ + cos θ = `sqrt(2)`
Choose the correct alternative:
If cos pθ + cos qθ = 0 and if p ≠ q, then θ is equal to (n is any integer)
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
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.