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 = `sqrt(3)`
Find the general solution of the following equation:
cot θ = 0.
Find the general solution of the following equation:
cosec θ = - √2.
Find the general solution of the following equation:
tan3θ = 3 tanθ.
Find the general solution of the following equation:
cosθ + sinθ = 1.
State whether the following equation have solution or not?
cos 2θ = – 1
In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.
In ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos "A"/(2)`.
Select the correct option from the given alternatives:
The general solution of sec x = `sqrt(2)` is ______.
Select the correct option from the given alternatives:
If cos pθ = cos qθ, p ≠ q, then ______.
If `sqrt3 cos x − sin x = 1`, then general value of x is ______.
If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______.
Find the general solutions of the following equation:
sin θ - cos θ = 1
In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.
If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.
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 `tan^-1 1/2 = 1/3 tan^-1 11/2`
Show that `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2 = (5pi)/6`.
Prove the following:
`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0
Find the principal solutions of cosec x = 2
Find the principal solutions of sin x = `-1/2`
If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
`int 1/(sin x * cos x)` dx = ?
`int (sin (log x))^2/x` log x dx = ?
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
`[sin (tan^-1 3/4)]^2 + [sin(tan^-1 4/3)]^2 = ?`
If f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
The value of sin 18° is ______.
The general solution of the equation tan θ tan 2θ = 1 is given by ______
If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.
The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` is ______.
Which of the following equation has no solution?
The number of principal solutions of tan 2θ = 1 is ______.
The general solution of the equation tan2 x = 1 is ______.
With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.
The general solution to cos100x – sin100x = 1 is ______.
The general solution of cot 4x = –1 is ______.
If `sin^-1 4/5 + cos^-1 12/13` = sin–1α, then find the value of α.
If tan3θ = cotθ, then θ =
