(3 cos x + 7) (-2 sin x - 1) = 0

Dear Student,

 

In the given problem, the left hand side can only be equal to zero when either one of the two expressions are zero or both of them are zero.

 

Hence, if the first expression is zero, then

3cosx + 7 = 0

=> cosx = -7/3

 

However, we know that the range of values that cos function can attain are from -1 to 1. Therefore, cosx can not attain -7/3 value for any value of x. So, the first expression can not be zero for any value of x.

 

If the second expression is zero, then

- 2sinx - 1 = 0

=> sinx = -1/2

=> x = sin^-1(-1/2)

 

We know that sin attains negative values in third and fourth quadrant. hence, the possible values of x can be (180^o + 30^o) or (360^o - 30^o).

 

Therefore, the value of x can be either 210^o and 330^o.

 

 

Regards,

Topperlearning