Advertisements
Advertisements
Question
Select the correct option from the given alternatives:
If cos pθ = cos qθ, p ≠ q, then ______.
Options
θ = `(2npi)/(p +- q)`
θ = 2nπ
θ = 2nπ ± p
θ = 2nπ ± q
Advertisements
Solution
If cos pθ = cos qθ, p ≠ q, then, θ = `bb(underline((2npi)/(p +- q))`
Explanation:
Given, cos pθ = cos qθ
cos pθ – cos qθ = 0
`2sin((pθ + qθ)/2) sin((pθ - qθ)/2)` = 0 ...(cos C – cos D)
`sin((pθ + qθ)/2)` = 0 or `sin ((pθ - qθ)/2)` = 0
`(pθ + qθ)/2` = nπ or `(pθ - qθ)/2` = nπ
θ = `(2nπ)/((p + q))` or `(2nπ)/((p - q))` = θ
∴ θ = `(2nπ)/(p +- q)`
RELATED QUESTIONS
Find the principal solution of the following equation:
Sec θ = `(2)/sqrt(3)`
Find the principal solution of the following equation:
cot θ = 0
Find the principal solution of the following equation:
sin θ = `-1/2`
Find the general solution of the following equation:
tan θ = - 1
Find the general solution of the following equation:
sin θ = tan θ
With the usual notations prove that `2{asin^2 "C"/(2) + "c"sin^2 "A"/(2)}` = a – b + c.
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 = _______
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 ______.
If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ 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:
tan 3θ = - 1
Find the general solutions of the following equation:
`tan theta = - sqrt3`
Find the general solutions of the following equation:
`tan^2 theta = 3`
With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`
If sin-1(1 - x) - 2 sin-1x = `pi/2`, then find the value of x.
Show that `tan^-1 1/2 - tan^-1 1/4 = tan^-1 2/9`.
Show that `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2 = (5pi)/6`.
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`
The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______
Find the principal solutions of sin x = `-1/2`
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
`int (sin (log x))^2/x` log x dx = ?
`[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.
The principal solutions of cot x = `sqrt3` are ______.
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
The general solution of the equation tan θ tan 2θ = 1 is given by ______
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 ______.
The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` is ______.
The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is ______.
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
The general solution to cos100x – sin100x = 1 is ______.
The general solution of cot 4x = –1 is ______.
