Advertisements
Advertisements
प्रश्न
Find the principal solutions of cosec x = 2
उत्तर
cosec x = 2
∴ cosec x = `"cosec" (pi/6)` and cosec x = `"cosec" (pi - pi/6)`
= `"cosec" ((5pi)/6)`
such that `0 ≤ pi/6 < 2pi` and `0 ≤ (5pi)/6 < 2pi`
∴ The required principal solutions are x = `pi/6` and x = `(5pi)/6`.
संबंधित प्रश्न
Find the principal solution of the following equation:
Sec θ = `(2)/sqrt(3)`
Find the general solution of the following equation:
sin 2θ = `1/2`
Find the general solution of the following equation:
tan `(2θ)/(3) = sqrt3`.
Find the general solution of the following equation:
cot 4θ = – 1
Find the general solution of the following equation:
4sin2θ = 1.
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 have solution or not?
3 tanθ = 5
In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.
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:
The principal solutions of equation sin θ = `- 1/2` are ______.
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 polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are
Select the correct option from the given alternatives:
In ΔABC, ac cos B - bc cos A = _______
`"cos"^-1 ("cos" (7pi)/6)` = _________.
Select the correct option from the given alternatives:
The value of cot (tan-12x + cot-12x) is
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 ______.
Select the correct option from the given alternatives:
In any ΔABC, if acos B = bcos A, then the triangle is
Find the general solutions of the following equation:
`tan^2 theta = 3`
In Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin "C"/2` .
With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`
State whether the following equation has a solution or not?
3 sin θ = 5
Show that `tan^-1 1/2 - tan^-1 1/4 = tan^-1 2/9`.
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
Show that `2 cot^(-1) 3/2 + sec^(-1) 13/12 = π/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
If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.
`cos^-1 (cos (4pi)/3)` = ______.
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?
Which of the following equations has no solution?
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 sin θ + cos θ = 1, then the general value of θ is ______.
The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.
General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.
If `sin^-1 4/5 + cos^-1 12/13` = sin–1α, then find the value of α.
