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

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Answer: Zero

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.

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