Home
Class 12
MATHS
The number of solutions of the equation ...

The number of solutions of the equation `cos^(2)((pi)/(3)cos x - (8pi)/(3))=1` in the interval `[0,10pi]` is

A

1

B

3

C

5

D

7

Text Solution

Verified by Experts

The correct Answer is:
C
`cos^(2)((pi)/(3)cos. X-(8pi)/(3))=1`
`rArr (pi)/(3)cos. X-(8pi)/(3)=k pi, (k in Z)`
`rArr cos x = 3k + 8, k in Z`
`rArr cos x = -1`, when `k = -3`
`rArr` there are 5 solutions for `x in [0, 10pi]`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the number of solution of the equation 2x=3pi (1-cos x) .

Find the number of real solution of the equation (cos x)^(5)+(sin x)^(3)=1 in the interval [0, 2pi]

The number of solutions of the equation 16(sin^(5)x +cos^(5)x)=11(sin x + cos x) in the interval [0,2pi] is

The -number of solutions of the equation cos(pisqrt(x-4)cos(pi sqrtx)=1 is

The number of solutions of the equation cos6x+tan^2x+cos(6x)tan^2x=1 in the interval [0,2pi] is (a) 4 (b) 5 (c) 6 (d) 7

The number of solutions of the equation 3^(2sec^(2)x)+1=10.3^(tan^(2)x) in the interval [0,2pi] is

The number of solution of the equation int_(-2)^(1)|cos x|dx=0,0ltxlt(pi)/(2) , is

Number of solution(s) of the equation (sinx)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27x)=0 in the interval (0,pi/4) is____________

The number of solution of the equation 2sin^(-1)((2x)/(1+x^(2)))-pi x^(3)=0 is equal to

The number of solution of the equation |sin x|=|cos 3x| in [-2pi,2pi] is