Advertisements
Advertisements
प्रश्न
Solve the following equation:
cosx + sin x = cos 2x + sin 2x
Advertisements
उत्तर
\[\cos x + \sin x = \cos2x + \sin2x\]
\[ \Rightarrow \cos2x - \cos x + \sin2x - \sin x = 0\]
\[ \Rightarrow - 2\sin\frac{3x}{2}\sin\frac{x}{2} + 2\cos\frac{3x}{2}\sin\frac{x}{2} = 0\]
\[ \Rightarrow 2\sin\frac{x}{2}\left( \cos\frac{3x}{2} - \sin\frac{3x}{2} \right) = 0\]
\[ \Rightarrow 2 \sin\frac{x}{2} = 0\text{ or }\cos\frac{3x}{2} - \sin\frac{3x}{2} = 0\]
\[ \Rightarrow \sin\frac{x}{2} = 0\text{ or }\cos\frac{3x}{2} = \sin\frac{3x}{2}\]
\[ \Rightarrow \frac{x}{2} = n\pi\text{ or }\tan\frac{3x}{2} = 1\]
\[ \Rightarrow x = 2n\pi\text{ or }\tan\frac{3x}{2} = \tan\frac{\pi}{4}\]
\[ \Rightarrow x = 2n\pi\text{ or }\frac{3x}{2} = n\pi + \frac{\pi}{4}\]
\[ \Rightarrow x = 2n\pi\text{ or }3x = 2n\pi + \frac{\pi}{2}\]
\[ \Rightarrow x = 2n\pi\text{ or }x = \frac{2n\pi}{3} + \frac{\pi}{6}, n \in \mathbb{Z}\]
APPEARS IN
संबंधित प्रश्न
Find the general solution of cosec x = –2
Find the general solution of the equation sin x + sin 3x + sin 5x = 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 \[\tan x = \frac{a}{b},\] show 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:
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 sec \[x = x + \frac{1}{4x}\], then sec x + tan x =
If \[0 < x < \frac{\pi}{2}\], and if \[\frac{y + 1}{1 - y} = \sqrt{\frac{1 + \sin x}{1 - \sin x}}\], then y is equal to
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 \[cosec x + \cot x = \frac{11}{2}\], then tan x =
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:
`cosec x = 1 + cot x`
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:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].
Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]
and cos 2x are in A.P.
Write the number of points of intersection of the curves
If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]
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:
cot θ = `sqrt(3)`
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
In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.
