Home
Class 12
MATHS
Find the number of solution of [cosx]+|s...

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

Text Solution

Verified by Experts

We have `[cos x]+|sin x|=1`
Now, `-1 le cos x le 1`
`:.` Possible values of `[cos x]` are `0, 1, -1`
Case I :
`[cos x]=-1` or `cos x in [-1, 0)`
`:. -1 +|sin x|=1`
`rArr |sin x|=2` (not possible)
Case II :
`[cos x]=0` or `cos x in [0, 1)`
`:. |sin x|=1`
`rArr x=(3pi)/2, (5pi)/2`
Case III :
`[cos x]=1` or `cos x=1`
`:. |sin x|=0`
`:. x=2pi`
Hence, there are three solutions.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.1|12 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.2|6 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|34 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

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

Find the number of solution of the equations |cos x |=[x] , (where [.] denotes the greatest integer function ).

The number of solutions of [sin x]+cos x=1 in x in[0,6 pi] where [ ] denotes greatest integer function

The number of solutions of [sin x+ cos x]=3+ [- sin x]+[-cos x] (where [.] denotes the greatest integer function), x in [0, 2pi] , is

The number of solutions of [sinx+cosx]=3+[-sinx]+[-cosx](w h e r e[] denotes the greatest integer function), x in [0,2pi] , is 0 (b) 4 (c) infinite (d) 1

Find number of solutions for equation [sin^(-1)x]=x-[x] , where [.] denotes the greatest integer function.

Number of solutions of the equation x^(2)-2=[sinx] , where [.] denotes the greatest integer function, is

f(x)=1+[cos x]x in 0<=x<=(pi)/(2) (where [.] denotes greatest integer function)

Let f(x)=(-1)^([x]) where [.] denotes the greatest integer function),then

Number of solutions of sin x=[x] where [.] denotes the greatest integer function is