Advertisements
Advertisements
प्रश्न
Solve the following equation:
Advertisements
उत्तर
Now,
\[3 ( \cos^2 x - \sin^2 x) - \sqrt{3} \sin2x = 0\]
\[ \Rightarrow 3 \cos2x - \sqrt{3} \sin2x = 0\]
\[ \Rightarrow \sqrt{3} (\sqrt{3} \cos2x - \sin2x) = 0\]
\[ \Rightarrow (\sqrt{3} \cos2x - \sin2x) = 0\]
\[ \Rightarrow \frac{\sin2x}{\cos2x} = \sqrt{3} \]
\[ \Rightarrow \tan2x = \tan \frac{\pi}{3}\]
\[ \Rightarrow 2x = n\pi + \frac{\pi}{3}, n \in Z\]
\[ \Rightarrow x = \frac{n\pi}{2} + \frac{\pi}{6}, n \in Z\]
APPEARS IN
संबंधित प्रश्न
Find the general solution of cosec x = –2
Find the general solution of the equation sin 2x + cos x = 0
If \[cosec x - \sin x = a^3 , \sec x - \cos x = b^3\], then prove that \[a^2 b^2 \left( a^2 + b^2 \right) = 1\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[2 T_6 - 3 T_4 + 1 = 0\]
Prove that:
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
Prove that:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]
Prove that
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
If tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to
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 θ + sec θ =ex, then cos θ equals
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:
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]
Write the number of points of intersection of the curves
If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.
If \[4 \sin^2 x = 1\], then the values of x are
General solution of \[\tan 5 x = \cot 2 x\] is
Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`
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 cos2x + 1 = – 3 cos 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:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
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 a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.
Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0
The minimum value of 3cosx + 4sinx + 8 is ______.
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
