Advertisements
Advertisements
Question
Write the general solutions of tan2 2x = 1.
Advertisements
Solution
Given:
\[\tan^2 2x = 1\]
\[ \Rightarrow \tan 2x = \tan \frac{\pi}{4}\]
\[ \Rightarrow 2x = n\pi + \frac{\pi}{4}\]
\[ \Rightarrow x = \frac{n\pi}{2} + \frac{\pi}{8}, n \in Z\]
Hence, the general solution of the equation is
\[\frac{n\pi}{2} + \frac{\pi}{8}, n \in Z .\]
APPEARS IN
RELATED QUESTIONS
Find the general solution of cosec x = –2
Find the general solution of the equation sin 2x + cos x = 0
If \[\cot x \left( 1 + \sin x \right) = 4 m \text{ and }\cot x \left( 1 - \sin x \right) = 4 n,\] \[\left( m^2 + n^2 \right)^2 = mn\]
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: \[\tan\frac{11\pi}{3} - 2\sin\frac{4\pi}{6} - \frac{3}{4} {cosec}^2 \frac{\pi}{4} + 4 \cos^2 \frac{17\pi}{6} = \frac{3 - 4\sqrt{3}}{2}\]
Prove that:
\[\sec\left( \frac{3\pi}{2} - x \right)\sec\left( x - \frac{5\pi}{2} \right) + \tan\left( \frac{5\pi}{2} + x \right)\tan\left( x - \frac{3\pi}{2} \right) = - 1 .\]
In a ∆ABC, prove that:
If tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to
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 \[f\left( x \right) = \cos^2 x + \sec^2 x\], then
The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] is
The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is
Find the general solution of the following equation:
Find the general solution of the following equation:
Find the general solution of the following equation:
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:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[\cot x + \tan x = 2\]
Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0
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.
The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]
The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval
If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are
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 sin α + cos α = b, then sin 2α 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 ______.
