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

State whether the following equation have solution or not? 3 tanθ = 5

Advertisements
Advertisements

प्रश्न

State whether the following equation have solution or not?

3 tanθ = 5

बेरीज
Advertisements

उत्तर

Yes, it has a solution.

Because tanθ can take any real value, from

3 tanθ = 5 ⇒ tanθ = `5/3`, which is possible

θ = tan−1 `(5/3) + npi,` n ∈ Z

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Trigonometric Functions - Exercise 3.1 [पृष्ठ ७५]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 3 Trigonometric Functions
Exercise 3.1 | Q 8.4 | पृष्ठ ७५

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:

`sqrt(3)` cosecθ + 2 = 0 


Find the general solution of the following equation :

cosθ = `sqrt(3)/(2)`


Find the general solution of the following equation:

cosec θ = - √2.


Find the general solution of the following equation:

tan θ = - 1


State whether the following equation have solution or not?

cos 2θ = – 1


State whether the following equation has a solution or not?

cos2θ = – 1.


In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.


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 general solution of sec x = `sqrt(2)` is ______.


Select the correct option from the given alternatives:

If cos pθ = cos qθ, p ≠ q, then ______.


The principal value of sin–1 `(- sqrt3/2)` is ______.


Select the correct option from the given alternatives:

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


If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.


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


If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.


If sin-1(1 - x) - 2 sin-1x =  `pi/2`, then find the value of x.


Show that `cot^-1  1/3 - tan^-1  1/3 = cot^-1  3/4`.


Show that `cos^-1  sqrt3/2 + 2 sin^-1  sqrt3/2 = (5pi)/6`.


Prove the following:

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


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 cosec x = 2


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


`cos^-1 (cos  (4pi)/3)` = ______.


If x + y = `pi/2`, then the maximum value of sin x. sin y is.


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 value of θ in the equation `2sqrt(3) cos theta = tan theta` is ______.


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


The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` is ______.


Find the principal solutions of cot θ = 0


If y = `(2sinα)/(1 + cosα + sinα)`, then value of `(1 - cos α + sin α)/(1 + sin α)` is ______.


Which of the following equation has no solution?


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 ______.


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.


If tan θ + sec θ = `sqrt(3)`, find the general value of θ.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×