Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
sin θ = tan θ.
उत्तर
sin θ = tan θ
∴ sinθ = `"sinθ"/"cosθ"`
∴ sinθ cosθ = sinθ
∴ sinθ cosθ – sinθ = 0
∴ sinθ (cosθ – 1) = 0
∴ either sinθ = 0 or cosθ – 1 = 0
∴ either sinθ = 0 or cosθ = 1
∴ either sinθ = 0 or cosθ = cos0 ...[∵ cos 0 = 1]
The general solution of sin θ = 0 is θ = nπ, n ∈ Z and cosθ = cos α is θ = 2nπ ± α, where n ∈ Z.
∴ the required general solution is given by
θ = nπ, n ∈ Z or θ = 2nπ ± 0, n ∈ Z
∴ θ = nπ, n ∈ Z or θ = 2nπ, n ∈ Z.
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation:
cosθ = `(1)/(2)`
Find the principal solution of the following equation :
cot θ = `sqrt(3)`
Find the general solution of the following equation:
sec θ = `sqrt(2)`.
Find the general solution of the following equation:
cot 4θ = – 1
Select the correct option from the given alternatives:
If cos pθ = cos qθ, p ≠ q, then ______.
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.
Find the general solutions of the following equation:
`tan theta = - sqrt3`
Find the general solutions of the following equation:
sin2 θ - cos2 θ = 1
Find the general solutions of the following equation:
sin θ - cos θ = 1
If 2 tan-1(cos x) = tan-1(2 cosec x), then find the value of x.
Prove the following:
`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0
Find the principal solutions of tan x = `-sqrt(3)`
If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.
`cos^-1 (cos (4pi)/3)` = ______.
`int 1/(sin x * cos x)` dx = ?
The general solution of sec θ = `sqrt2` is
`int (sin (log x))^2/x` log x dx = ?
If f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?
If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?
If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ is ________.
Which of the following equations has no solution?
The value of θ in (π, 2π) satisfying the equation sin2θ - cos2θ = 1 is ______
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______
If sin θ + cos θ = 1, then the general value of θ is ______.
The general solution of cot θ + tan θ = 2 is ______.
If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.
The general value of θ in the equation `2sqrt(3) cos theta = tan theta` is ______.
The equation 3sin2x + 10 cos x – 6 = 0 is satisfied, if ______.
Find the principal solutions of cot θ = 0
If y = `(2sinα)/(1 + cosα + sinα)`, then value of `(1 - cos α + sin α)/(1 + sin α)` is ______.
The general solution of the equation tan2 x = 1 is ______.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
If tan θ + sec θ = `sqrt(3)`, find the general value of θ.
