CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Prove that the determinant $$\begin{vmatrix} x & sin \theta & cos \theta \\ - sin \theta & - x & 1 \\ cos \theta & 1 & x \end{vmatrix}$$ is independent of $$\theta$$.


Solution

$$\begin{vmatrix} x & sin \theta & cos \theta \\ - sin \theta & - x & 1 \\ cos \theta & 1 & x \end{vmatrix}$$

$$= x(-x^{2}-1)- sin \theta (-x sin\theta - cos\theta)+cos \theta (- sin\theta +x cos \theta )$$

$$= -x^{3}-x+x sin^{2}\theta + sin\theta cos\theta -sin\theta cos\theta +x cos^{2}\theta $$

$$= -x^{3}-x+x(sin^{2}\theta +cos^{2}\theta )$$

$$=-x^{3}-x+x$$

$$=-x^{3}$$ ( Which is Independent of $$\theta $$ )

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image