Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
sin θ = tan θ
Advertisements
उत्तर
sin θ = tan θ
tan θ = `sin theta/cos theta`
sin θ = `sin theta/cos theta`
Multiply both sides by cos θ
sin θ ⋅ cos θ = sin θ
sin θ cos θ − sin θ = 0
⇒ sin θ(cos θ − 1) = 0
sin θ(cos θ − 1) = 0
Case 1: sin θ = 0
sinθ = 0 ⇒ θ = nπ, where n ∈ Z
Case 2: cosθ = 1
cos θ = 1
⇒ θ = 2nπ, where n ∈ Z
Consider excluded values (where cos θ = 0)
sin θ = `sintheta/costheta`
cos θ = 0
⇒ theta = `pi/2 + npi`, where n ∈ Z
θ = nπ, where n ∈ Z
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation :
cot θ = `sqrt(3)`
Find the principal solution of the following equation:
tan θ = – 1
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
Find the general solution of the following equation:
4 cos2 θ = 3
Find the general solution of the following equation:
tan3θ = 3 tanθ.
State whether the following equation has a solution or not?
2sinθ = 3
In ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos "A"/(2)`.
In Δ ABC, prove that a3 sin(B – C) + b3sin(C – A) + c3sin(A – B) = 0
In ΔABC, if a cos A = b cos B then prove that the triangle is either a right angled or an isosceles traingle.
Select the correct option from the given alternatives:
The principal solutions of equation sin θ = `- 1/2` are ______.
Select the correct option from the given alternatives:
The principal solutions of equation cot θ = `sqrt3` are ______.
Select the correct option from the given alternatives:
The general solution of sec x = `sqrt(2)` is ______.
If `sqrt3`cos x - sin x = 1, then general value of x is ______.
Select the correct option from the given alternatives:
In ΔABC if c2 + a2 – b2 = ac, then ∠B = ____.
Select the correct option from the given alternatives:
The value of cot (tan-12x + cot-12x) is
Select the correct option from the given alternatives:
If tan-1(2x) + tan-1(3x) = `pi/4`, then x = _____
The principal value branch of sec-1x is ______.
If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.
Find the principal solutions of the following equation:
tan 3θ = - 1
Find the general solutions of the following equation:
`tan^2 theta = 3`
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
With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`
State whether the following equation has a solution or not?
3 sin θ = 5
If 2 tan-1(cos x) = tan-1(2 cosec x), then find the value of x.
If tan-12x + tan-13x = `pi/4`, then find the value of x.
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
Show that `2 cot^(-1) 3/2 + sec^(-1) 13/12 = π/2`
Find the principal solutions of cosec x = 2
Find the principal solutions of cos 2𝑥 = 1
If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.
`int 1/(sin x * cos x)` dx = ?
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
The principal solutions of cot x = `sqrt3` are ______.
Which of the following equations has no solution?
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
If function
f(x) = `x - |x|/x, x < 0`
= `x + |x|/x, x > 0`
= 1, x = 0, then
The value of θ in (π, 2π) satisfying the equation sin2θ - cos2θ = 1 is ______
Which of the following is true in a triangle ABC?
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 ______.
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
The general solution to cos100x – sin100x = 1 is ______.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
