English

Which of the following is incorrect? - Mathematics

Advertisements
Advertisements

Question

Which of the following is incorrect?

Options

  • \[\sin x = - \frac{1}{5}\]

     

  • cos x = 1

  • \[\sec x = \frac{1}{2}\]

     

  • tan x = 20

MCQ

Solution

`bb(sec x = 1/2)`

Explanation:

\[\sin x = - \frac{1}{5}\] is correct as \[- 1 \leq \sin x \leq 1\]

cos x = 1 is correct as cos x = 1 is correct as

\[\sec x = \frac{1}{2}\] is not correct as \[\sec x \in ( - \infty , - 1] \cup [1, \infty )\]
tan x = 20 is correct as tan x can take any real value.
Hence, the correct answer is option \[\sec x = \frac{1}{2}\].
shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Trigonometric Functions - Exercise 5.5 [Page 43]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 5 Trigonometric Functions
Exercise 5.5 | Q 25 | Page 43

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the principal and general solutions of the equation `tan x = sqrt3`


Find the principal and general solutions of the equation sec x = 2


Find the general solution of the equation sin 2x + cos x = 0


Find the general solution for each of the following equations sec2 2x = 1– tan 2x


If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x


If \[\tan x = \frac{a}{b},\] show that

\[\frac{a \sin x - b \cos x}{a \sin x + b \cos x} = \frac{a^2 - b^2}{a^2 + b^2}\]

If \[cosec x - \sin x = a^3 , \sec x - \cos x = b^3\], then prove that \[a^2 b^2 \left( a^2 + b^2 \right) = 1\]


If \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]


In a ∆A, B, C, D be the angles of a cyclic quadrilateral, taken in order, prove that cos(180° − A) + cos (180° + B) + cos (180° + C) − sin (90° + D) = 0


Find x from the following equations:
\[x \cot\left( \frac{\pi}{2} + \theta \right) + \tan\left( \frac{\pi}{2} + \theta \right)\sin \theta + cosec\left( \frac{\pi}{2} + \theta \right) = 0\]


Prove that:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]


Prove that:

\[\tan\frac{5\pi}{4}\cot\frac{9\pi}{4} + \tan\frac{17\pi}{4}\cot\frac{15\pi}{4} = 0\]

 


If tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to


\[\sec^2 x = \frac{4xy}{(x + y )^2}\] is true if and only if

 


If x sin 45° cos2 60° = \[\frac{\tan^2 60^\circ cosec30^\circ}{\sec45^\circ \cot^{2^\circ} 30^\circ}\], then x =

 

If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to


Find the general solution of the following equation:

\[\sin 2x = \cos 3x\]

Find the general solution of the following equation:

\[\tan 2x \tan x = 1\]

Solve the following equation:

\[\sin x + \sin 2x + \sin 3x + \sin 4x = 0\]

Solve the following equation:

\[\tan 3x + \tan x = 2\tan 2x\]

Solve the following equation:
4sinx cosx + 2 sin x + 2 cosx + 1 = 0 


Solve the following equation:
3tanx + cot x = 5 cosec x


Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].


If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.

 

Write the number of points of intersection of the curves

\[2y = - 1 \text{ and }y = cosec x\]

Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].


If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.


If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.


A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval


The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]


Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

2 sin2x + 1 = 3 sin x


Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1


Solve the following equations:
cos 2θ = `(sqrt(5) + 1)/4`


Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval


Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to


Solve the equation sin θ + sin 3θ + sin 5θ = 0


Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`


Find the general solution of the equation sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×