Advertisements
Advertisements
प्रश्न
Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`
उत्तर
sin θ = `-1/sqrt(2)`
We know that principal of sin θ lies in `[ - pi/2, pi/2]`
sin θ = `- 1/sqrt(2 < 0`
∴ The principal value of sin θ lies in the IV quadrant.
sin θ = `- 1/sqrt(2)`
= `- sin(pi/4)`
sin θ = `sin (- pi/4)`
Hence θ = `- pi/4` is the principal solution.
The general solution is
θ = nπ + (– 1)n . `( pi/4)`, n ∈ Z
θ = `"n"pi + (- 1)^("n" + 1) * pi/4`, n ∈ Z
APPEARS IN
संबंधित प्रश्न
If \[x = \frac{2 \sin x}{1 + \cos x + \sin x}\], then prove that
Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]
Prove that
In a ∆ABC, prove that:
cos (A + B) + cos C = 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 sec \[x = x + \frac{1}{4x}\], then sec x + tan x =
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
If x sin 45° cos2 60° = \[\frac{\tan^2 60^\circ cosec30^\circ}{\sec45^\circ \cot^{2^\circ} 30^\circ}\], then x =
If tan θ + sec θ =ex, then cos θ equals
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
\[\cot x + \tan x = 2\]
Solve the following equation:
sin x tan x – 1 = tan x – sin x
If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 sin2x + 1 = 3 sin x
Solve the following equations:
sin 5x − sin x = cos 3
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
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 sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x
