Advertisements
Advertisements
प्रश्न
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
sin4x = sin2x
Advertisements
उत्तर
sin4x – sin2x = 0
sin2 x (sin2 x – 1) = 0
sin2 x [– (1 – sin2 x)] = 0
sin2x × – cos2x = 0
– sin2x cos2x = 0
(sin x cos x)2 = 0
`(1/2 xx 2 sin cos x)^2` = 0
`1/4 sin 2x` = 0
sin 2x = 0
The general solution is
2x = nπ, n ∈ Z
x = `("n"pi)/2`, n ∈ Z
When n = 0, x = `(0 xx pi)/2` = 0 ∉ (0°, 360°)
When n = 1, x = `pi/2` = ∈ (0°, 360°)
When n = 2, x = `(2pi)/2` = π ∈ (0°, 360°)
When n = 3, x = `(3pi)/2` = ∈ (0°, 360°)
When n = 4, x = `(4pi)/2` = 2π ∉ (0°, 360°)
∴ The values of x are `pi/2`, π, `(3pi)/2`
APPEARS IN
संबंधित प्रश्न
If \[\sin x + \cos x = m\], then prove that \[\sin^6 x + \cos^6 x = \frac{4 - 3 \left( m^2 - 1 \right)^2}{4}\], where \[m^2 \leq 2\]
Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]
Prove that
Prove that
In a ∆ABC, prove that:
Find x from the following equations:
\[x \cot\left( \frac{\pi}{2} + \theta \right) + \tan\left( \frac{\pi}{2} + \theta \right)\sin \theta + cosec\left( \frac{\pi}{2} + \theta \right) = 0\]
If tan A + cot A = 4, then tan4 A + cot4 A is equal to
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:
`cosec x = 1 + cot x`
Solve the following equation:
3tanx + cot x = 5 cosec x
Write the solution set of the equation
Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].
The smallest value of x satisfying the equation
The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 sin2x + 1 = 3 sin x
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 ______.
