Advertisements
Advertisements
प्रश्न
Solve the following equations:
sin θ + cos θ = `sqrt(2)`
Advertisements
उत्तर
Divide each term by `sqrt(2)`
`1/sqrt(2) sin theta + 1/sqrt(2) cos theta = sqrt(2)/sqrt(2)`
`sin pi/4 sin theta + cos pi/4 cos theta` = 1
`cos theta * cos pi/4 + sin theta * sin pi/4` = 1
`cos (theta - pi/4)` = 1
`cos (theta - pi/4)` = cos θ
The general solution is
`theta - pi/4` = 2nπ, n ∈ Z
θ = `2"n"pi + pi/4`, n ∈ Z
θ = `(8"n"pi + pi)/4`, n ∈ Z
θ = `(8"n" + 1) pi/4`, n ∈ Z
APPEARS IN
संबंधित प्रश्न
Find the general solution of the equation cos 4 x = cos 2 x
Find x from the following equations:
\[x \cot\left( \frac{\pi}{2} + \theta \right) + \tan\left( \frac{\pi}{2} + \theta \right)\sin \theta + cosec\left( \frac{\pi}{2} + \theta \right) = 0\]
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 x is an acute angle and \[\tan x = \frac{1}{\sqrt{7}}\], then the value of \[\frac{{cosec}^2 x - \sec^2 x}{{cosec}^2 x + \sec^2 x}\] is
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
If tan A + cot A = 4, then tan4 A + cot4 A is equal to
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:
Solve the following equation:
\[2 \sin^2 x = 3\cos x, 0 \leq x \leq 2\pi\]
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
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°
2 cos2x + 1 = – 3 cos x
Solve the following equations:
sin 5x − sin x = cos 3
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
