Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
sin 2θ = `1/2`
Advertisements
उत्तर
The general solution of sin θ = sin α is
θ = nπ + (– 1)nα, n ∈ Z.
Now,
sin 2θ = `1/2`
∴ sin 2θ = `sin pi/(6) ...[ ∵ sin pi/(6) = (1)/(2)]`
∴ the required general solution is given by
2θ = nπ + (- 1)n `(pi/6)`, n ∈ Z.
i.e. θ = `(npi)/(2) + (- 1)^n (pi/12)`,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:
cot θ = 0
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:
tan θ = `(1)/(sqrt(3))`
Find the general solution of the following equation:
cos 4θ = cos 2θ
State whether the following equation have solution or not?
cos 2θ = – 1
State whether the following equation has a solution or not?
cos2θ = – 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)`.
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.
With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .
Select the correct option from the given alternatives:
If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are
If `sqrt3 cos x − sin x = 1`, then general value of x is ______.
Select the correct option from the given alternatives:
In ΔABC, ac cos B - bc cos A = _______
Select the correct option from the given alternatives:
The value of cot (tan-12x + cot-12x) is
The principal value branch of sec-1x is ______.
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:
cot θ = 0
Find the general solutions of the following equation:
sin θ - cos θ = 1
If sin-1(1 - x) - 2 sin-1x = `pi/2`, 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 - tan^-1 1/4 = tan^-1 2/9`.
Show that `2 cot^(-1) 3/2 + sec^(-1) 13/12 = π/2`
Prove the following:
`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0
If x, y, z are positive, then prove that
`tan^-1 (("x - y")/(1 + "xy")) + tan^-1 (("y - z")/(1 + "yz")) + tan^-1 (("z - x")/(1 + "zx")) = 0`
Find the principal solutions of cos 2𝑥 = 1
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
The general solution of sec θ = `sqrt2` is
`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 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 principal solutions of cot x = `sqrt3` are ______.
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 general solution of cot θ + tan θ = 2 is ______.
The general value of θ in the equation `2sqrt(3) cos theta = tan theta` is ______.
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.
The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is ______.
The number of principal solutions of tan 2θ = 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 tan θ + sec θ = `sqrt(3)`, find the general value of θ.
