Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
उत्तर
We have:
⇒ \[\sin9x - \sin x = 0\]
⇒ \[2 \sin \left( \frac{9x - x}{2} \right) \cos \left( \frac{9x + x}{2} \right) = 0\]
⇒ \[\sin \frac{8x}{2} = 0\] or \[\cos \frac{10x}{2} = 0\]
⇒ \[\sin 4x = 0\] or \[\cos 5x = 0\]
⇒ \[4x = n\pi\]
\[n \in Z\] or \[5x = (2n + 1)\frac{\pi}{2}\],
\[n \in Z\]
⇒ \[x = \frac{n\pi}{4}\],
\[n \in Z\] or \[x = (2n + 1)\frac{\pi}{10}\],
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 \[x = \frac{2 \sin x}{1 + \cos x + \sin x}\], then prove that
Prove the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[\frac{T_3 - T_5}{T_1} = \frac{T_5 - T_7}{T_3}\]
Prove that:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]
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:
\[\tan 4\pi - \cos\frac{3\pi}{2} - \sin\frac{5\pi}{6}\cos\frac{2\pi}{3} = \frac{1}{4}\]
If tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to
If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to
sin6 A + cos6 A + 3 sin2 A cos2 A =
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
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
Which of the following is incorrect?
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:
\[\sin^2 x - \cos x = \frac{1}{4}\]
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[2 \sin^2 x = 3\cos x, 0 \leq x \leq 2\pi\]
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
Solve the following equation:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]
Solve the following equation:
3tanx + cot x = 5 cosec x
If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is
Solve the following equations:
sin 5x − sin x = cos 3
Solve the following equations:
2 cos2θ + 3 sin θ – 3 = θ
Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1
Choose the correct alternative:
If tan 40° = λ, then `(tan 140^circ - tan 130^circ)/(1 + tan 140^circ * tan 130^circ)` =
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
Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0
The minimum value of 3cosx + 4sinx + 8 is ______.
