# Get Answers to all your Questions

#### provide solution for RD Sharma maths class 12 chapter 5 Determinants exercise  Fill in the blanks question 30

Hint: Here, we use basic concept of determinant of matrix.

Given: $\left[\begin{array}{ccc} \sin A & \cos A & \sin A+\cos B \\ \sin B & \cos A & \sin B+\cos B \\ \sin C & \cos A & \sin C+\cos B \end{array}\right]=0$

Solution: Let’s take sin A, sin B and sin C common from respectively 1st , 2nd and 3rd row

$\sin A \sin B \sin C\left[\begin{array}{lll} 1 & \cos A & 1+\cos B \\ 1 & \cos A & 1+\cos B \\ 1 & \cos A & 1+\cos B \end{array}\right]$

Here, all rows are same

According to properties of determinants, if there are 2 or more rows are same then, value of determinants is zero.

So, Answer is zero.