हिंदी

State whether the following equation has a solution or not? cos2θ = – 1. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

State whether the following equation has a solution or not?

cos2θ = – 1.

योग

उत्तर

cos2θ = – 1

This is not possible because cos2θ ≥ 0 for any θ.

∴ cos2θ = – 1 does not have any solution.

shaalaa.com
Trigonometric Equations and Their Solutions
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Trigonometric Functions - Exercise 3.1 [पृष्ठ ७५]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
अध्याय 3 Trigonometric Functions
Exercise 3.1 | Q 8.2 | पृष्ठ ७५
बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
अध्याय 3 Trigonometric Functions
Miscellaneous exercise 3 | Q 3.2 | पृष्ठ १०९

संबंधित प्रश्न

Find the principal solution of the following equation:

sin θ = `-1/2`


Find the general solution of the following equation:

4sin2θ = 1.


Find the general solution of the following equation:

cos 4θ = cos 2θ


Find the general solution of the following equation:

sin θ = tan θ.


State whether the following equation has a solution or not?

2sinθ = 3


With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c.


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:

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


Select the correct option from the given alternatives:

If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______


Select the correct option from the given alternatives:

If tan-1(2x) + tan-1(3x) = `pi/4`, then x = _____


Select the correct option from the given alternatives:

`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______


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


Find the principal solutions of the following equation:

cot θ = 0


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


In ΔABC, prove that `("a - b")^2 cos^2  "C"/2 + ("a + b")^2 sin^2  "C"/2 = "c"^2`


In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.


If tan-12x + tan-13x = `pi/4`, then find the value of x.


Show that `tan^-1  1/2 - tan^-1  1/4 = tan^-1  2/9`.


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


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


`cos^-1 (cos  (4pi)/3)` = ______.


The value of tan 57°- tan 12°- tan 57° tan 12° is ______.


The general solution of sec θ = `sqrt2` is


If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is


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


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


The principal solutions of cot x = `sqrt3` are ______.


Which of the following equations has no solution?


The value of `tan^-1  1/3 + tan^-1  1/5 + tan^-1  1/7 + tan^-1  1/8` is ______.


The value of sin 18° is ______.


The value of θ in (π, 2π) satisfying the equation sin2θ - cos2θ = 1 is ______ 


The general solution of the equation tan θ tan 2θ = 1 is given by ______ 


The general solution of the equation tan2 x = 1 is ______.


If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.


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


If `sin^-1  4/5 + cos^-1  12/13` = sin–1α, then find the value of α.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×