मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Find the principal solutions of tan x = -3 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find the principal solutions of tan x = `-sqrt(3)`

बेरीज
Advertisements

उत्तर

tan x = `-sqrt(3)`

∴ tan x = `-tan (pi/3)`

∴ tan x = `tan (pi - pi/3)`

= `tan ((2pi)/3)` and  tan x = `tan (2pi - pi/3)`

= `tan ((5pi)/3)`

such that `0 ≤ (2pi)/3 < 2pi` and `0 ≤ (5pi)/3 < 2pi`

∴ The required principal solutions are x = `(2pi)/3` and x = `(5pi)/3`.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.3: Trigonometric Functions - Short Answers I

संबंधित प्रश्‍न

Find the principal solution of the following equation: 

cosθ = `(1)/(2)`


Find the principal solution of the following equation: 

Sec θ = `(2)/sqrt(3)`


Find the principal solution of the following equation :

cot θ = `sqrt(3)`


Find the principal solution of the following equation: 

tan θ = – 1


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:

cot θ = 0.


Find the general solution of the following equation:

cot 4θ = – 1


Find the general solution of the following equation:

4sin2θ = 1.


Find the general solution of the following equation:

cos 4θ = cos 2θ


State whether the following equation have solution or not?

3 tanθ = 5


Select the correct option from the given alternatives:

The principal solutions of equation cot θ = `sqrt3` are ______.


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


`"cos"^-1 ("cos" (7pi)/6)` = _________.


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:

`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____


`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 general solutions of the following equation:

`tan^2 theta = 3`


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`


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`.


Prove the following:

`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0


If `tan^-1 "x" + tan^-1 "y" + tan^-1 "z" = pi/2,` then show that xy + yz + zx = 1


Find the principal solutions of cos 2𝑥 = 1


Find the principal solutions of sin x = `-1/2`


`int 1/(sin x * cos x)` dx = ?


`int (sin (log x))^2/x` log x dx = ?


`[sin (tan^-1  3/4)]^2 + [sin(tan^-1  4/3)]^2 = ?`


If f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?


If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ 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?


The equation 3sin2x + 10 cos x – 6 = 0 is satisfied, if ______.


Find the principal solutions of cot θ = 0


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 ______.


Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.


If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×