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  • Please solve RD Sharma class 12 chapter Determinants exercise 5.1 question 2 subquestion (ii) maths textbook solution

Please solve RD Sharma class 12 chapter Determinants exercise 5.1 question 2 subquestion (ii) maths textbook solution

Answers (1)

Answer:

cos^{2}\theta +sin^{2} \theta =1

Hint:

Determinant matrix must be square (i.e. same number of rows and columns)

Given:

\begin{aligned} \left|\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right|\\ \end{aligned}

Solution:

\begin{aligned} &\begin{aligned} &\mathrm{D}=\mathrm{a}_{11} \times \mathrm{C}_{11}+\mathrm{a}_{21} \times \mathrm{C}_{21} \\ &=\cos \theta(\cos \theta)+(-\sin \theta \times(-\sin \theta)) \\ &=\cos ^{2} \theta+\sin ^{2} \theta \\ &=1 \end{aligned} \end{aligned}

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