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1) Find the number of integral values of k for which the equation 7cosx+5sinx = 2k+1 has a solution 2) Fine the general value of x satisfying the equation √3sinx+cosx = √3 3) Find the interval in which the solution of the equation cos^2theta+sin theta+1 = 0 lies in. 4) If 5cos2theta + 2cos^2 theta/2+1 = 0, -π 5) Find the number of solutions of the equation 5sec theta-13 = 12tan theta in [0,2π] 6) Find the number of solutions of the equation cos(π√x-4) cos(π√x) = 1 7) What is the solution of the equation cos^2(π/3 cosx - 8π/3) = 1?

1) Find the number of integral values of k for which the equation 7cosx+5sinx = 2k+1 has a solution
2) Fine the general value of x satisfying the equation √3sinx+cosx = √3
3) Find the interval in which the solution of the equation cos^2theta+sin theta+1 = 0 lies in.
4) If 5cos2theta + 2cos^2 theta/2+1 = 0, -π
5) Find the number of solutions of the equation 5sec theta-13 = 12tan theta in [0,2π]
6) Find the number of solutions of the equation cos(π√x-4) cos(π√x) = 1
7) What is the solution of the equation cos^2(π/3 cosx - 8π/3) = 1?
 

Grade:11

1 Answers

Arun
25750 Points
4 years ago
Dear student
 
Please ask only ome question in o e thread.
 
1.)
 

Maxinmum value of 7cosx+5sinx=√(72+52)=√74=8.6

and minimum value is -8.6

so it will vary between -8.6 to 8.6

2k+1 is an odd integer. 

hence 2k will lies bwteen -9.6 to 7.6

hence k lies between – 4.8 to 3.8

and corresponding values of k will be -4,-3,-2,-1,0,1,2,3

hence there are 8 values of k

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