Home
Class 11
MATHS
No. of solutions of cosx∣1+sinx∣ ...

No. of solutions of ` cosx∣1+sinx∣ ` , `0≤x≤3π `, is

Text Solution

AI Generated Solution

To find the number of solutions for the equation \( \cos x \cdot |1 + \sin x| = 0 \) in the interval \( 0 \leq x \leq 3\pi \), we can break it down step by step. ### Step 1: Understand the equation The equation can be rewritten as: \[ \cos x \cdot |1 + \sin x| = 0 \] This implies that either \( \cos x = 0 \) or \( |1 + \sin x| = 0 \). ...
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION

    ALLEN|Exercise EXERCISE (JM)|8 Videos
  • BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION

    ALLEN|Exercise EXERCISE (S-1)|41 Videos
  • BASIC MATHS LOGARITHIM TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION

    ALLEN|Exercise ILLUSTRATIONS|39 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    ALLEN|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

The number of distinct solutions of secθ+tanθ= √3 , 0≤θ≤3π , is

Number of solution of sinx cosx-3cosx+4sinx-13 gt 0 in [0,2pi] is equal to

The number of solution of 2cosx=|sinx| where x in [0.4pi] is/are

The number of solutions of the equation |cosx-sinx|=2cosx in [0,2pi] is (A) 1 (B) 2 (C) 3 (D) 4

Find the number of solution of [cosx]+|sinx|=1, x inpilt=xlt=3pi (where [ ] denotes the greatest integer function).

Recall that sinx + cosx =u (say) and sin x cosx =v (say) are connected by (sinx +cosx)^(2) = sin^(2)x + cos^(2)x+2sin cosx rArr u^(2) = 1+2v rArr v=(u^(2)-1)/(2) It follows that any rational integral function of sinx + cosx , and sinx cosx i.e., R(sinx + cosx, sinx cosx) , or in our notation R(u,v) can be transformed to R(u, (u^(2)-1)/2) . Thus, to solve an equation of the form R(u,v)=0 , we form a polynomial equation in u and than look for solutions. The solution set of sinx + cosx -2sqrt(2) sin x cosx=0 is completely described by

Total number of solutions of sin^2x−sinx−1=0 in [−2π,2π] is equal to:

Find the number of solution of log_(1/2) |sinx| = 2 - log_(1/2) |cosx|, x in [0, 2pi]

Find the number of solution of log_(1/2) |sinx| = 2 - log_(1/2) |cosx|, x in [0, 2pi]

The number of the solutions of the equation 3sinx + 4cosx-x^2-16 = 0 is