Advertisements
Advertisements
Question
Find the general solution of the following equation:
Advertisements
Solution
We have:
\[\Rightarrow \tan2x = \frac{1}{\tan x}\]
\[ \Rightarrow \tan2x = \cot x\]
\[ \Rightarrow \tan2x = \tan \left( \frac{\pi}{2} - x \right)\]
\[ \Rightarrow 2x = n\pi + \left( \frac{\pi}{2} - x \right), n \in Z\]
\[ \Rightarrow 3x = n\pi + \frac{\pi}{2}, n \in Z\]
\[ \Rightarrow x = \frac{n\pi}{3} + \frac{\pi}{6}, n \in Z\]
APPEARS IN
RELATED QUESTIONS
Prove the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]
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:
cos (A + B) + cos C = 0
In a ∆ABC, prove that:
Prove that:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]
If \[\frac{\pi}{2} < x < \pi, \text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}}\] 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 \[\frac{3\pi}{4} < \alpha < \pi, \text{ then }\sqrt{2\cot \alpha + \frac{1}{\sin^2 \alpha}}\] is equal to
sin2 π/18 + sin2 π/9 + sin2 7π/18 + sin2 4π/9 =
Which of the following is incorrect?
Which of the following is correct?
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:
Solve the following equation:
`cosec x = 1 + cot x`
Solve the following equation:
cosx + sin x = cos 2x + sin 2x
Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]
Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]
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 number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].
The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
If \[4 \sin^2 x = 1\], then the values of x are
A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is
The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
cos 2x = 1 − 3 sin x
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 the equation sin θ + sin 3θ + sin 5θ = 0
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
