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  • Provide solution for RD Sharma maths class 12 chapter Determinants exercise multiple choise question 6

Provide solution for RD Sharma maths class 12 chapter Determinants exercise multiple choise question 6

Answers (1)

Answer:

Correct option (a)

Hint:

        Suppose\: \: nx=u,\: (n+1)x=v,\: (n+2)x=w

then solve determinant.

Given:

        \begin{vmatrix} a^{2} &a &1 \\ cos\: nx &cos(n+1)x &cos(n+2)x \\ sin\: nx &sin(n+1)x &sin(n+2)x \end{vmatrix}

Solution:

        \begin{vmatrix} a^{2} &a &1 \\ cos\: nx &cos(n+1)x &cos(n+2)x \\ sin\: nx &sin(n+1)x &sin(n+2)x \end{vmatrix}

Putting\: \: nx=u,\: (n+1)x=v,\: (n+2)x=w,

Then we have,

                \begin{vmatrix} a^{2} &a &1 \\ cos\: u &cos\, v &cos\, w \\ sin\: u &sin\, v&sin\, w \end{vmatrix}

        =a^{2}(cos\, v\, sin\, w-sin\, v\, cos\, w)-a(cos\, u\, sin\, w-sin\, u\, cos\, w)+1(cos\, u\, sin\, v-cos\, v\, sin\, u)

                =a^{2}sin(w-v)-a\, sin(w-u)+sin(v-u)

                =a^{2}sin\, x-a\, sin2x+sin\, x

Hence, it is independent of n.

Posted by

Gurleen Kaur

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