Advertisements
Advertisements
Question
Find the general solutions of the following equation:
`tan^2 theta = 3`
Advertisements
Solution
The general solution of tan2θ = tan2α is θ = nπ ± α, n ∈ Z.
Now, tan2 θ = 3 = `(sqrt3)^2`
∴ tan2 θ = `(tan pi/3)^2 ....[because "tan" pi/3 = sqrt3]`
∴ tan2 θ = `tan^2 (pi)/3`
∴ the required general solution is
∴ θ = `"n"pi +- (pi)/3,` n ∈ Z.
APPEARS IN
RELATED QUESTIONS
Find the principal solution of the following equation:
tan θ = – 1
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:
cot 4θ = – 1
Find the general solution of the following equation:
cos 4θ = cos 2θ
Find the general solution of the following equation:
sin θ = tan θ
Find the general solution of the following equation:
tan3θ = 3 tanθ.
State whether the following equation have solution or not?
cos 2θ = – 1
State whether the following equation has a solution or not?
cos2θ = – 1.
State whether the following equation has a solution or not?
2sinθ = 3
In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.
In ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos "A"/(2)`.
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 cos pθ = cos qθ, p ≠ q, then ______.
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:
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)` = ______
If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.
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`
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
Show that `2 cot^(-1) 3/2 + sec^(-1) 13/12 = π/2`
If cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.
Find the principal solutions of cos 2𝑥 = 1
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 1/(sin x * cos x)` dx = ?
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
The general solution of sec θ = `sqrt2` is
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
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 ______
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 the equation tan θ tan 2θ = 1 is given by ______
The general solution of cot θ + tan θ = 2 is ______.
If y = `(2sinα)/(1 + cosα + sinα)`, then value of `(1 - cos α + sin α)/(1 + sin α)` is ______.
If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.
The general solution to cos100x – sin100x = 1 is ______.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
