Advertisements
Advertisements
प्रश्न
Write the general solutions of tan2 2x = 1.
उत्तर
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
संबंधित प्रश्न
Find the principal and general solutions of the equation sec x = 2
Find the general solution of the equation sin 2x + cos x = 0
Find the general solution for each of the following equations sec2 2x = 1– tan 2x
If \[\cot x \left( 1 + \sin x \right) = 4 m \text{ and }\cot x \left( 1 - \sin x \right) = 4 n,\] \[\left( m^2 + n^2 \right)^2 = mn\]
Prove that: tan 225° cot 405° + tan 765° cot 675° = 0
Prove that
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
Prove that:
If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
If tan θ + sec θ =ex, then cos θ equals
If sec x + tan x = k, cos x =
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:
Solve the following equation:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]
Solve the following equation:
\[\sin x - 3\sin2x + \sin3x = \cos x - 3\cos2x + \cos3x\]
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
Write the set of values of a for which the equation
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 smallest value of x satisfying the equation
If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
If \[\cot x - \tan x = \sec x\], then, x is equal to
A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
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
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0
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 a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.
