Advertisements
Advertisements
Question
Find the general solution of the following equation:
Advertisements
Solution
We have:
⇒ \[\sin2x = \sin \frac{\pi}{3}\]
⇒ \[2x = n\pi + ( - 1 )^n \frac{\pi}{3}\]
⇒ \[x = \frac{n\pi}{2} + ( - 1 )^n \frac{\pi}{6}\],
APPEARS IN
RELATED QUESTIONS
Find the general solution of cosec x = –2
Find the general solution of the equation cos 3x + cos x – cos 2x = 0
Find the general solution of the equation sin 2x + cos x = 0
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
If \[\tan x = \frac{b}{a}\] , then find the values of \[\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}\].
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 \[\frac{T_3 - T_5}{T_1} = \frac{T_5 - T_7}{T_3}\]
Find x from the following equations:
\[cosec\left( \frac{\pi}{2} + \theta \right) + x \cos \theta \cot\left( \frac{\pi}{2} + \theta \right) = \sin\left( \frac{\pi}{2} + \theta \right)\]
Prove that:
If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then x2 + y2 + z2 is independent of
If tan x + sec x = \[\sqrt{3}\], 0 < x < π, then x is equal to
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
sin2 π/18 + sin2 π/9 + sin2 7π/18 + sin2 4π/9 =
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:
\[\sin x + \cos x = \sqrt{2}\]
Solve the following equation:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]
and cos 2x are in A.P.
If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.
The smallest value of x satisfying the equation
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
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
sin4x = sin2x
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0
Solve the following equations:
cos 2θ = `(sqrt(5) + 1)/4`
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 a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
