Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
tan θ = - 1
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:
Sec θ = `(2)/sqrt(3)`
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation:
sec θ = `sqrt(2)`.
Find the general solution of the following equation:
4cos2θ = 3.
In ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos "A"/(2)`.
In Δ ABC, prove that a3 sin(B – C) + b3sin(C – A) + c3sin(A – B) = 0
With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .
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:
The value of cot (tan-12x + cot-12x) is
Select the correct option from the given alternatives:
`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______
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:
cot θ = 0
In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.
State whether the following equation has a solution or not?
3 sin θ = 5
If sin-1(1 - x) - 2 sin-1x = `pi/2`, then find the value of x.
Prove the following:
`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0
If cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
The principal solutions of cot x = `sqrt3` are ______.
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
If 4 sin-1x + 6 cos-1 x = 3π then x = ______.
The general solution of sin 2x = cos 2x is ______
Which of the following is true in a triangle ABC?
If sin θ + cos θ = 1, then the general value of θ is ______.
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
If y = `(2sinα)/(1 + cosα + sinα)`, then value of `(1 - cos α + sin α)/(1 + sin α)` is ______.
The number of principal solutions of tan 2θ = 1 is ______.
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.
Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.
The general solution to cos100x – sin100x = 1 is ______.
The general solution of cot 4x = –1 is ______.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
If tan θ + sec θ = `sqrt(3)`, find the general value of θ.
