Advertisements
Advertisements
Question
Find the general solution of the following equation:
sin θ = tan θ
Advertisements
Solution
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
RELATED QUESTIONS
Find the principal solution of the following equation:
cot θ = 0
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation :
cosθ = `sqrt(3)/(2)`
Find the general solution of the following equation:
cot θ = 0.
Find the general solution of the following equation:
sec θ = `sqrt(2)`.
Find the general solution of the following equation:
cosec θ = - √2.
Find the general solution of the following equation:
tan θ = - 1
Find the general solution of the following equation:
tan `(2θ)/(3) = sqrt3`
Find the general solution of the following equation:
cot 4θ = – 1
Find the general solution of the following equation:
4 cos2 θ = 3
State whether the following equation have solution or not?
cos 2θ = – 1
With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .
If `sqrt3 cos x − sin x = 1`, then general value of x is ______.
If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to
Select the correct option from the given alternatives:
The value of cot (tan-12x + cot-12x) is
The principal value of sin–1 `(- sqrt3/2)` is ______.
Select the correct option from the given alternatives:
If tan-1(2x) + tan-1(3x) = `pi/4`, then x = _____
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
Select the correct option from the given alternatives:
In any ΔABC, if acos B = bcos A, then the triangle is
Find the principal solutions of the following equation:
sin 2θ = `-1/2`
Find the principal solutions of the following equation:
tan 3θ = - 1
In Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin "C"/2` .
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
Prove the following:
`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0
If cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.
The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______
Find the principal solutions of sin x = `-1/2`
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
`int 1/(sin x * cos x)` dx = ?
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
Which of the following equations has no solution?
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
The value of sin 18° is ______.
If 4 sin-1x + 6 cos-1 x = 3π then x = ______.
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______
The general solution of sin 2x = cos 2x is ______
The general solution of the equation tan θ tan 2θ = 1 is given by ______
The general solution of cot θ + tan θ = 2 is ______.
The general value of θ in the equation `2sqrt(3) cos theta = tan theta` is ______.
The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.
The number of principal solutions of tan 2θ = 1 is ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.
With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.
Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.
The general solution to cos100x – sin100x = 1 is ______.
