Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
tan θ = - 1
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the principal solution of the following equation:
cot θ = 0
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation :
cosθ = `sqrt(3)/(2)`
State whether the following equation have solution or not?
3 tanθ = 5
In Δ ABC, prove that a3 sin(B – C) + b3sin(C – A) + c3sin(A – B) = 0
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 sin θ = `- 1/2` are ______.
Select the correct option from the given alternatives:
The general solution of sec x = `sqrt(2)` is ______.
Select the correct option from the given alternatives:
If cos pθ = cos qθ, p ≠ q, then ______.
If `sqrt3`cos x - sin x = 1, then general value of x is ______.
Select the correct option from the given alternatives:
In Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are
Find the general solutions of the following equation:
`tan^2 theta = 3`
Find the general solutions of the following equation:
sin θ - cos θ = 1
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`
In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.
If sin-1(1 - x) - 2 sin-1x = `pi/2`, then find the value of x.
Show that `tan^-1 1/2 - tan^-1 1/4 = tan^-1 2/9`.
Show that `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2 = (5pi)/6`.
Find the principal solutions of cosec x = 2
Find the principal solutions of sin x − 1 = 0
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.
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
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
If 4 sin-1x + 6 cos-1 x = 3π then x = ______.
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 cosec x = `-sqrt2` is ______
Find the principal solutions of cot θ = 0
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.
The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is ______.
General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.
The general solution of the equation tan2 x = 1 is ______.
If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
The general solution to cos100x – sin100x = 1 is ______.
