Advertisements
Advertisements
प्रश्न
Find the principal solution of the following equation:
cot θ = 0
Advertisements
उत्तर
The given equation is cot θ = 0 which is same as
tan θ = ∞
We know that,
tan `π/2` = ∞ and tan (π + θ) = tan θ
∴ `tan (π/2) = tan (π + π/2) = tan ((3π)/2)`
∴ `tan (π/2) = tan ((3π)/2) = ∞`, where,
`0 < π/2 < 2π and 0 < (3π)/2 < 2π`
∴ cot θ = 0, i.e., tan θ = ∞ gives
`tan θ = tan (π/2) = tan ((3π)/2)`
∴ `θ = π/2 "and" θ = (3π)/2`
Hence, the required principal solution are `θ = π/2 "and" θ = (3π)/2`.
Notes
Answer in the textbook is incorrect.
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 general solution of the following equation:
tan θ = - 1
Find the general solution of the following equation:
4 cos2 θ = 3
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 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 cot θ = `sqrt3` are ______.
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 ______.
Select the correct option from the given alternatives:
In Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are
Select the correct option from the given alternatives:
In ΔABC if c2 + a2 – b2 = ac, then ∠B = ____.
`"cos"^-1 ("cos" (7pi)/6)` = _________.
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:
`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______
`cos[tan^-1 1/3 + tan^-1 1/2]` = ______
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:
sin 2θ = `-1/2`
If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.
If sin-1(1 - x) - 2 sin-1x = `pi/2`, then find the value of x.
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
Prove the following:
`cos^-1 "x" = pi + 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`
If `tan^-1 "x" + tan^-1 "y" + tan^-1 "z" = pi/2,` then show that xy + yz + zx = 1
The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______
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 ______.
`[sin (tan^-1 3/4)]^2 + [sin(tan^-1 4/3)]^2 = ?`
If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ is ________.
The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.
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 ______.
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
The value of sin 18° is ______.
The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` is ______.
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
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 ______.
The general solution to cos100x – sin100x = 1 is ______.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
If tan3θ = cotθ, then θ =
