Find the principal solutions of the following equation: cot 2θ = 0. - Mathematics and Statistics

Advertisements
Advertisements
Sum

Find the principal solutions of the following equation:

cot 2θ = 0.

Advertisements

Solution

`{π/4, (3π)/4, (5π)/4, (7π)/4}`.

  Is there an error in this question or solution?
Chapter 3: Trigonometric Functions - Miscellaneous exercise 3 [Page 108]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Trigonometric Functions
Miscellaneous exercise 3 | Q 2.3 | Page 108

RELATED QUESTIONS

If `sin^-1(1-x) -2sin^-1x = pi/2` then x is

  1. -1/2
  2. 1
  3. 0
  4. 1/2
 

If `tan^-1((x-1)/(x-2))+cot^-1((x+2)/(x+1))=pi/4; `


Show that `2sin^-1(3/5) = tan^-1(24/7)`


Show that:

`cos^(-1)(4/5)+cos^(-1)(12/13)=cos^(-1)(33/65)`


Find the principal value of `tan^(-1) (-sqrt3)`


Find the principal value of  `cos^(-1) (-1/2)`


Find the principal value of tan−1 (−1)


Find the principal value of  `cos^(-1) (-1/sqrt2)`


Find the principal value of `cosec^(-1)(-sqrt2)`


Find the value of  `tan^(-1)(1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)`


Find the value of `cos^(-1) (1/2) + 2 sin^(-1)(1/2)`


Show that `tan^-1  ((sqrt(1 + x) - sqrt(1 - x))/(sqrt(1 + x) + sqrt(1 - x))) = pi/4 - 1/2 cos^-1 x`, for `- 1/sqrt2 <= x <= 1`


`sin^-1  1/2-2sin^-1  1/sqrt2`


`sin^-1{cos(sin^-1  sqrt3/2)}`


Find the domain of the following function:

`f(x)=sin^-1x^2`

 


Find the domain of the following function:

`f(x) = sin^-1x + sinx`


Find the domain of the following function:

`f(x)sin^-1sqrt(x^2-1)`


Find the domain of the following function:

`f(x)=sin^-1x+sin^-1 2x`


If `sin^-1 x + sin^-1 y+sin^-1 z+sin^-1 t=2pi` , then find the value of x2 + y2 + z2 + t2 


Evaluate the following:

`tan^-1 1+cos^-1 (-1/2)+sin^-1(-1/2)`


Evaluate the following:

`tan^-1(-1/sqrt3)+tan^-1(-sqrt3)+tan^-1(sin(-pi/2))`


Find the set of values of `cosec^-1(sqrt3/2)`


Evaluate the following:

`cot^-1  1/sqrt3-\text(cosec)^-1(-2)+sec^-1(2/sqrt3)`


Evaluate the following:

`\text(cosec)^-1(-2/sqrt3)+2cot^-1(-1)`


Solve for x:
`tan^-1 [(x-1),(x-2)] + tan^-1 [(x+1),(x+2)] = x/4`


Evaluate: tan `[ 2 tan^-1  (1)/(2) – cot^-1 3]`


In ΔABC, if a = 18, b = 24, c = 30 then find the values of cosA


In ΔABC, if a = 18, b = 24, c = 30 then find the values of sin `A/2`.


In ΔABC, if a = 18, b = 24, c = 30 then find the values of cos `A/2`


In ΔABC, if a = 18, b = 24, c = 30 then find the values of tan `A/2`


In ΔABC, if a = 18, b = 24, c = 30 then find the values of A(ΔABC)


In ΔABC, if a = 18, b = 24, c = 30 then find the values of sinA


In ΔABC prove that `(b + c - a) tan  "A"/(2) = (c + a - b)tan  "B"/(2) = (a + b - c)tan  "C"/(2)`.


Find the principal value of the following: cosec- 1(2)


Find the principal value of the following: tan-1(– 1)


Find the principal value of the following: tan- 1( - √3)


Find the principal value of the following: sin-1 `(1/sqrt(2))`


Find the principal value of the following: cos- 1`(-1/2)`


Evaluate the following:

`tan^-1(1) + cos^-1(1/2) + sin^-1(1/2)`


Evaluate the following:

`tan^-1 sqrt(3) - sec^-1 (-2)`


Prove the following: 

`sin^-1(1/sqrt(2)) -3sin^-1(sqrt(3)/2) = -(3π)/(4)`


Prove the following:

`cos^-1(3/5) + cos^-1(4/5) = pi/(2)`


Prove the following:

`tan^-1(1/2) + tan^-1(1/3) = pi/(4)`


Prove the following: 

`2tan^-1(1/3) = tan^-1(3/4)`


Prove the following:

`tan^-1["cosθ + sinθ"/"cosθ - sinθ"] = pi/(4) + θ, if θ ∈ (- pi/4, pi/4)`


Prove the following:

`tan^-1[sqrt((1 - cosθ)/(1 + cosθ))] = θ/(2)`, if θ ∈ (– π, π).


In ΔABC, prove the following:

`"cos A"/"a" + "cos B"/"b" + "cos C"/"c" = ("a"^2 + "b"^2 + "c"^2)/(2"abc")`


Find the principal solutions of the following equation:

sin 2θ = `− 1/(sqrt2)`


Find the principal solutions of the following equation:
tan 5θ = -1


sin−1x − cos−1x = `pi/6`, then x = ______


The principal value of sin−1`(1/2)` is ______


`tan^-1(tan  (7pi)/6)` = ______


If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______


Prove that `2 tan^-1 (3/4) = tan^-1(24/7)`


Evaluate:

`sin[cos^-1 (3/5)]`


If tan−1x + tan−1y + tan−1z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1


Prove that cot−1(7) + 2 cot−1(3) = `pi/4`


Show that `sin^-1(3/5)  + sin^-1(8/17) = cos^-1(36/85)`


Prove that `2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4`


Find the principal value of the following:

tan-1 (-1)


Find the principal value of the following:

cosec-1 (2)


Show that `tan^-1 (1/2) + tan^-1 (2/11) = tan^-1 (3/4)`


Solve: tan-1 (x + 1) + tan-1 (x – 1) = `tan^-1 (4/7)`


Evaluate:

`cos[tan^-1 (3/4)]`


Evaluate: sin`[1/2 cos^-1 (4/5)]`


Evaluate: `cos (sin^-1 (4/5) + sin^-1 (12/13))`


Show that `sin^-1 (- 3/5) - sin^-1 (- 8/17) = cos^-1 (84/85)`


Find the principal value of `sin^-1  1/sqrt(2)`


Find the principal value of `cos^-1  sqrt(3)/2`


Find the principal value of cosec–1(– 1)


Find the principal value of `sec^-1 (- sqrt(2))`


Find the principal value of `tan^-1 (sqrt(3))`


A man standing directly opposite to one side of a road of width x meter views a circular shaped traffic green signal of diameter ‘a’ meter on the other side of the road. The bottom of the green signal Is ‘b’ meter height from the horizontal level of viewer’s eye. If ‘a’ denotes the angle subtended by the diameter of the green signal at the viewer’s eye, then prove that α = `tan^-1 (("a" + "b")/x) - tan^-1 ("b"/x)`


Choose the correct alternative:
cos 2θ cos 2ϕ+ sin2 (θ – ϕ) – sin2 (θ + ϕ) is equal to


The principle solutions of equation tan θ = -1 are ______ 


The value of cot (- 1110°) is equal to ______.


If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then θ = ______ 


If `tan^-1x + tan^-1y = (4pi)/5`, then `cot^-1x + cot^-1y` equals ______.


`sin{tan^-1((1 - x^2)/(2x)) + cos^-1((1 - x^2)/(1 + x^2))}` is equal to ______ 


The domain of the function defined by f(x) = sin–1x + cosx is ______.


The equation tan–1x – cot–1x = `(1/sqrt(3))` has ______.


If 2 tan–1(cos θ) = tan–1(2 cosec θ), then show that θ = π 4, where n is any integer.


All trigonometric functions have inverse over their respective domains.


When `"x" = "x"/2`, then tan x is ____________.


`"sin"^2 25° +  "sin"^2 65°` is equal to ____________.


`("cos" 8° -  "sin" 8°)/("cos" 8° +  "sin" 8°)`  is equal to ____________.


`"sin"  265° -  "cos"  265°` is ____________.


If `"cos"^-1  "x + sin"^-1  "x" = pi`, then the value of x is ____________.


`"cos"^-1 1/2 + 2  "sin"^-1  1/2` is equal to ____________.


`"tan"(pi/4 + 1/2 "cos"^-1 "x") + "tan" (pi/4 - 1/2 "cos"^-1 "x") =` ____________.


If tan-1 x – tan-1 y = tan-1 A, then A is equal to ____________.


`"cos" ["tan"^-1 {"sin" ("cot"^-1 "x")}]` is equal to ____________.


The equation of the tangent to the curve given by x = a sin3t, y = bcos3t at a point where t = `pi/2` is


If a = `(2sin theta)/(1 + costheta + sintheta)`, then `(1 + sintheta - costheta)/(1 + sintheta)` is 


If |Z1| = |Z2| and arg (Z1) + arg (Z2) = 0, then


Which of the following functions is inverse of itself?


The number of solutions of sin–1x + sin–1(1 – x) = cos–1x is


sin 6θ + sin 4θ + sin 2θ = 0, then θ =


If `sqrt(2)` sec θ + tan θ = 1, then the general value of θ is


If `(-1)/sqrt(2) ≤ x ≤ 1/sqrt(2)` then `sin^-1 (2xsqrt(1 - x^2))` is equal to


What is the value of `sin^-1(sin  (3pi)/4)`?


What will be the principal value of `sin^-1(-1/2)`?


What is the principal value of cosec–1(2).


`sin(tan^-1x), |x| < 1` is equal to


`2tan^-1 (cos x) = tan^-1 (2"cosec"  x)`, then 'x' will be equal to


what is the value of `cos^-1 (cos  (13pi)/6)`


Value of `sin(pi/3 - sin^1 (- 1/2))` is equal to


What is the values of `cos^-1 (cos  (7pi)/6)`


If f(x) = x5 + 2x – 3, then (f–1)1 (–3) = ______.


Find the principal value of `cot^-1 ((-1)/sqrt(3))`


If f'(x) = x–1, then find f(x)


Assertion (A): The domain of the function sec–12x is `(-∞, - 1/2] ∪ pi/2, ∞)`

Reason (R): sec–1(–2) = `- pi/4`


If θ = `sin^-1((2x)/(1 + x^2)) + cos^-1((1 - x^2)/(1 + x^2))`, for `x ≥ 3/2` then the absolute value of `((cosθ + tanθ + 4)/secθ)` is ______.


Consider f(x) = sin–1[2x] + cos–1([x] – 1) (where [.] denotes greatest integer function.) If domain of f(x) is [a, b) and the range of f(x) is {c, d} then `a + b + (2d)/c` is equal to ______. (where c < d) 


Let x = sin–1(sin8) + cos–1(cos11) + tan–1(tan7), and x = k(π – 2.4) for an integer k, then the value of k is ______.


Number of values of x satisfying the system of equations `sin^-1sqrt(2 + e^(-2x) - 2e^-x) + sec^-1sqrt(1 - x^2 + x^4) = π/2` and `5^(1+tan^-1x)` = 4 + [cos–1x] is ______ (where [.] denotes greatest integer function)


cos–1(cos10) is equal to ______.


`cot^-1(sqrt(cos α)) - tan^-1 (sqrt(cos α))` = x, then sin x = ______.


If x ∈ R – {0}, then `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2)))`


The value of cos (2cos–1 x + sin–1 x) at x = `1/5` is ______.


If tan–1 2x + tan–1 3x = `π/4`, then x = ______.


Derivative of `tan^-1(x/sqrt(1 - x^2))` with respect sin–1(3x – 4x3) is ______.


If y = `tan^-1  (sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))`, then `dy/dx` is equal to ______.


`sin[π/3 + sin^-1 (1/2)]` is equal to ______.


If sin–1x – cos–1x = `π/6`, then x = ______.


Prove that:

tan–1x + tan–1y = `π + tan^-1((x + y)/(1 - xy))`, provided x > 0, y > 0, xy > 1


The value of `tan(cos^-1  4/5 + tan^-1  2/3)` is ______.


Find the value of `sin(2cos^-1  sqrt(5)/3)`.


Solve for x:

5tan–1x + 3cot–1x = 2π


Share
Notifications



      Forgot password?
Use app×