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
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
If \[cosec x - \sin x = a^3 , \sec x - \cos x = b^3\], then prove that \[a^2 b^2 \left( a^2 + b^2 \right) = 1\]
Prove the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]
Prove that:
Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]
Prove that:
Prove that
Find x from the following equations:
\[x \cot\left( \frac{\pi}{2} + \theta \right) + \tan\left( \frac{\pi}{2} + \theta \right)\sin \theta + cosec\left( \frac{\pi}{2} + \theta \right) = 0\]
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 tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is
sin2 π/18 + sin2 π/9 + sin2 7π/18 + sin2 4π/9 =
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
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:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
Solve the following equation:
sin x tan x – 1 = tan x – sin x
Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]
If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
If \[4 \sin^2 x = 1\], then the values of x are
If \[\cot x - \tan x = \sec x\], then, x is equal to
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 cos2x + 1 = – 3 cos x
Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
Choose the correct alternative:
`(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x)` is equal to
Solve the equation sin θ + sin 3θ + sin 5θ = 0
Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.
