Question

the number of values of x such that cos3x+sin(2x-7π/6) =-2 and x £ [-12π, 14π] is​

Answer 1

Given  : cos3x+sin(2x-7π/6) =-2  

x ∈ [-12π, 14π]

To Find :  number of values of x s

Solution:

cos3x+sin(2x-7π/6) = - 2

only possible when

Cos3x  and  sin(2x-7π/6)  both are - 1

Cos3x =  - 1   => 3x = (2n +1)π

=> x =  (2n +1)π/3

sin(2x-7π/6)

=  Sin(2 (2n +1)π/3 - 7π/6)

= Sin( 4nπ/3  + 2π/3 - 7π/6)

= Sin( 4nπ/3  - 3π/6)

=Sin( 4nπ/3  -  π/2)

Hence n must be multiple of 3

n = 3k

so  x =  (2*3k +1)π/3

=> 2k + π/3

-12π ≤   2k + π/3   ≤ 14π

=> -36π ≤   6k + π    ≤ 42π

=> -37π ≤   6k     ≤ 41π

=> -6  ≤ k ≤ 6

Hence 13  Solutions

13 possible values of x

-35 π/3   to  37π/3  with   2π  

Learn More:

Number of positive integral solution of (x1+x2+x3) (y1+y2)=77 ...

https://brainly.in/question/8159987

Which of the following represents all possible values of M that are ...

https://brainly.in/question/20890003