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

Select the correct option from the given alternatives: "tan"(2"tan"^-1 (1/5) - pi/4) = ______ - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Select the correct option from the given alternatives:

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

पर्याय

  • `17/7`

  • `-17/7`

  • `7/17`

  • `-7/17`

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

`"tan"(2"tan"^-1 (1/5) - pi/4) = \underline(-7/17)`.

Explanation:

`tantheta = 1/5`

`tan(2theta) = (2tantheta)/(1-tan^2theta)`

`tan(2theta) = 2(1/5)/1-(1/5)^2 = (2/5)/(1-1/25) = (2/5)/(24/25) = 2/5 xx 25/24 = 50/120 = 5/12`

`tan(2theta) = 5/12`

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

`tan(2theta - pi/4) = (5/12 -1)/(1+5/12 xx 1) = ((5-12)/12)/(1+5/12) = (-7/12)/(17/12) = -7/17`

`=-7/17`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Trigonometric Functions - Miscellaneous exercise 3 [पृष्ठ १०८]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 3 Trigonometric Functions
Miscellaneous exercise 3 | Q 1.16 | पृष्ठ १०८

संबंधित प्रश्‍न

Find the principal solution of the following equation: 

Sec θ = `(2)/sqrt(3)`


Find the principal solution of the following equation:

cot θ = 0


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:

tan θ = `(1)/(sqrt(3))`


Find the general solution of the following equation:

cot 4θ = – 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.


State whether the following equation has a solution or not?

2sinθ = 3


With the usual notations prove that `2{asin^2  "C"/(2) + "c"sin^2  "A"/(2)}` = a – b + c.


In ΔABC, if a cos A = b cos B then prove that the triangle is either a right angled or an isosceles traingle.


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


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 ______.


If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to


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


The principal value of sin1 `(- sqrt3/2)` is ______.


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


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 general solutions of the following equation:

`tan theta = - sqrt3`


Find the general solutions of the following equation:

`tan^2 theta = 3`


Find the general solutions of the following equation:

sin θ - cos θ = 1


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


If x, y, z are positive, then prove that

`tan^-1 (("x - y")/(1 + "xy")) + tan^-1 (("y - z")/(1 + "yz")) + tan^-1 (("z - x")/(1 + "zx")) = 0`


The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______


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


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


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


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


If function

f(x) = `x - |x|/x, x < 0`
      = `x + |x|/x, x > 0`
      = 1, x = 0, then


The value of sin 18° is ______.


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


Find the principal solutions of cot θ = 0


If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.


The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ 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 ______.


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


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


The general solution to cos100x – sin100x = 1 is ______.


If tan3θ = cotθ, then θ =


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×