Prove that the determinant {:[( x, sin ...

Prove that the determinant ` {:[( x, sin theta ,cos theta ),( -sin theta , -x , 1),( cos theta , 1,x) ]:}` is independent of ` theta.

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Prove that the determinant Delta =|{:(x,,sintheta,,cos theta),(-sin theta,,-x,,1),(cos theta,,1,,x):}| is independent of theta .

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Knowledge Check

the solution of sin ^3 theta cos theta - sin theta cos^3 theta = 1/4 is

A

`((n pi)/(4)) +(-1)^n ((pi)/(8))`

B

`((n pi )/(2)) +-( (pi)/(8))`

C

`((npi)/(4))+ (-1)^(n+1) ((pi)/(8))`

D

`((n pi)/(8))+(-1) ^n ((pi)/(8))`

If A=[{:(cos theta, sin theta),(-sin theta, cos theta):}] then "A A"^(T) is :

A

A

B

`A^(T)`

C

I

D

0

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