Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • State True or False for the statements The determinant sinA cosA sinApluscosA is equal to zero.

State True or False for the statements

The determinant \left|\begin{array}{ccc} \sin A & \cos A & \sin A+\cos A \\ \sin B & \cos B & \sin B+\cos B \\ \sin C & \cos C & \sin C+\cos C \end{array}\right| is equal to zero.

Answers (1)

\left|\begin{array}{ccc} \sin A & \cos A & \sin A+\cos A \\ \sin B & \cos B & \sin B+\cos B \\ \sin C & \cos C & \sin C+\cos C \end{array}\right|

\\=\left|\begin{array}{ccc} \sin A & \cos A & \sin A \\ \sin B & \cos B & \sin B \\ \sin C & \cos C & \sin C \end{array}\right|+\left|\begin{array}{ccc} \sin A & \cos A & \cos A \\ \sin B & \cos B & \cos B \\ \sin C & \cos C & \cos C \end{array}\right|

We can see that columns are identical in both the matrix on Right hand side

 

Thus Determinant = 0

 

Statement in question is therefore true

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question