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:
`sqrt(3)` cosecθ + 2 = 0
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation:
tan θ = `(1)/(sqrt(3))`
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:
sin θ = tan θ
Find the general solution of the following equation:
cosθ + sinθ = 1.
State whether the following equation have solution or not?
cos 2θ = – 1
State whether the following equation has a solution or not?
2sinθ = 3
With the usual notations prove that `2{asin^2 "C"/(2) + "c"sin^2 "A"/(2)}` = a – b + c.
In Δ ABC, prove that a3 sin(B – C) + b3sin(C – A) + c3sin(A – B) = 0
Select the correct option from the given alternatives:
If cos pθ = cos qθ, p ≠ q, then ______.
Select the correct option from the given alternatives:
In Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are
`"cos"^-1 ("cos" (7pi)/6)` = _________.
Select the correct option from the given alternatives:
If tan-1(2x) + tan-1(3x) = `pi/4`, then x = _____
The principal value branch of sec-1x is ______.
If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.
Find the general solutions of the following equation:
`tan theta = - sqrt3`
In Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin "C"/2` .
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.
If sin-1(1 - x) - 2 sin-1x = `pi/2`, then find the value of x.
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
If cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.
Find the principal solutions of cosec x = 2
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
`int (sin (log x))^2/x` log x dx = ?
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
The general solution of sin 2x = cos 2x is ______
The general solution of the equation tan θ tan 2θ = 1 is given by ______
If sin θ + cos θ = 1, then the general value of θ is ______.
The equation 3sin2x + 10 cos x – 6 = 0 is satisfied, if ______.
If y = `(2sinα)/(1 + cosα + sinα)`, then value of `(1 - cos α + sin α)/(1 + sin α)` is ______.
General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.
Which of the following equation has no solution?
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 ______.
Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.
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 tan θ + sec θ = `sqrt(3)`, find the general value of θ.
If tan3θ = cotθ, then θ =
