Advertisements
Advertisements
Question
Find the general solution of the following equation:
tan θ = - 1
Solution
The general solution of tan θ = tan α is
θ = nπ + α, n ∈ Z.
Now, tan θ = – 1
∴ tan θ = - tan `pi/(4) .....[ ∵ tan pi/4 = 1]`
∴ tan θ = `tan(pi - pi/4)` ...[ ∵ tan(π - θ) = – tan θ]
∴ tan θ = `tan (3pi)/(4)`
∴ the required general solution is
θ = nπ + `(3pi)/(4)`, n ∈ Z.
APPEARS IN
RELATED QUESTIONS
Find the general solution of the following equation:
cot 4θ = – 1
Find the general solution of the following equation:
4cos2θ = 3.
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:
cosθ + sinθ = 1.
State whether the following equation has a solution or not?
cos2θ = – 1.
State whether the following equation have solution or not?
3 tanθ = 5
In ΔABC, if a cos A = b cos B then prove that the triangle is either a right angled or an isosceles traingle.
With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .
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 ______.
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)` = _________.
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)` = ______
Select the correct option from the given alternatives:
The principal value branch of sec-1x is
`"cos"["tan"^-1 1/3 + "tan"^-1 1/2]` = ______
Find the general solutions of the following equation:
`tan^2 theta = 3`
Find the general solutions of the following equation:
sin2 θ - cos2 θ = 1
Find the general solutions of the following equation:
sin θ - cos θ = 1
In ΔABC, prove that `("a - b")^2 cos^2 "C"/2 + ("a + b")^2 sin^2 "C"/2 = "c"^2`
If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
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))`
Find the principal solutions of cos 2𝑥 = 1
Find the principal solutions of tan x = `-sqrt(3)`
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
The number of solutions of `sin^2 theta = 1/2` in [0, π] 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 general solution of the equation tan θ tan 2θ = 1 is given by ______
Which of the following is true in a triangle ABC?
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
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.
