Advertisements
Advertisements
Question
Find the general solutions of the following equation:
`tan theta = - sqrt3`
Advertisements
Solution
The general solution of tan θ = tan α is
θ = nπ + α, n ∈ Z.
Now, tan θ = - `sqrt3`
∴ tan θ = - `tan pi/3 ....[because "tan" pi/3 = sqrt3]`
∴ tan θ = tan`(pi - pi/3) ...[because tan (pi - theta) = - tan theta]`
∴ tan θ = tan`(2pi)/3`
∴ the required general solution is
∴ θ = `"n"pi + (2pi)/3,` n ∈ Z
APPEARS IN
RELATED QUESTIONS
Find the principal solution of the following equation:
cosθ = `(1)/(2)`
Find the principal solution of the following equation :
cot θ = `sqrt(3)`
Find the principal solution of the following equation:
cot θ = 0
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:
cot 4θ = – 1
Find the general solution of the following equation:
4 cos2 θ = 3
In Δ ABC, prove that a3 sin(B – C) + b3sin(C – A) + c3sin(A – B) = 0
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:
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
If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______.
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
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]` = ______
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:
tan 3θ = - 1
Find the principal solutions of the following equation:
cot θ = 0
If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.
State whether the following equation has a solution or not?
3 sin θ = 5
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
Prove the following:
`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0
If | x | < 1, then prove that
`2 tan^-1 "x" = tan^-1 ("2x"/(1 - "x"^2)) = sin^-1 ("2x"/(1 + "x"^2)) = cos^-1 ((1 - "x"^2)/(1 + "x"^2))`
The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______
Find the principal solutions of sin x = `-1/2`
`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)` = ?
The general solution of sec θ = `sqrt2` is
`[sin (tan^-1 3/4)]^2 + [sin(tan^-1 4/3)]^2 = ?`
If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?
The principal solutions of cot x = `sqrt3` are ______.
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 general solution of sin 2x = cos 2x is ______
The general solution of the equation tan θ tan 2θ = 1 is given by ______
Which of the following is true in a triangle ABC?
If sin θ + cos θ = 1, then the general value of θ is ______.
The general solution of cot θ + tan θ = 2 is ______.
The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is ______.
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
The general solution to cos100x – sin100x = 1 is ______.
The general solution of cot 4x = –1 is ______.
If `sin^-1 4/5 + cos^-1 12/13` = sin–1α, then find the value of α.
