Advertisements
Advertisements
Question
Select the correct option from the given alternatives:
The general solution of sec x = `sqrt(2)` is ______.
Options
`2npi +- pi/4, n∈Z`
`2npi +- pi/2, n∈Z`
`npi +- pi/2, n∈Z`
`2npi +- pi/3, n∈Z`
Solution
The general solution of sec x = `sqrt(2)` is `bb(underline(2"n"pi +- pi/4, n∈Z))`.
RELATED QUESTIONS
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 2θ = `1/2`
Find the general solution of the following equation:
4sin2θ = 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.
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 cot θ = `sqrt3` are ______.
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 = ____.
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
`"cos"^-1 ("cos" (7pi)/6)` = _________.
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:
sin 2θ = `-1/2`
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`
In Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin "C"/2` .
In ΔABC, prove that `("a - b")^2 cos^2 "C"/2 + ("a + b")^2 sin^2 "C"/2 = "c"^2`
State whether the following equation has a solution or not?
3 sin θ = 5
If tan-12x + tan-13x = `pi/4`, then find the value of x.
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 cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.
The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______
Find the principal solutions of sin x − 1 = 0
Find the principal solutions of cos 2ЁЭСе = 1
Find the principal solutions of tan x = `-sqrt(3)`
`int 1/(sin x * cos x)` dx = ?
The general solution of sec θ = `sqrt2` is
If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
If function
f(x) = `x - |x|/x, x < 0`
= `x + |x|/x, x > 0`
= 1, x = 0, then
The value of θ in (π, 2π) satisfying the equation sin2θ - cos2θ = 1 is ______
The general solution of cot θ + tan θ = 2 is ______.
The general solution of 4sin2 x = 1 is ______.
The equation 3sin2x + 10 cos x – 6 = 0 is satisfied, if ______.
Find the principal solutions of cot θ = 0
General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.
The general solution of the equation tan2 x = 1 is ______.
Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.
