First slide

Applications of determinant

Question

$f (x) = |\begin{array}{l} \cos (x + α) & \cos (x + β) & \cos (x + r) \\ \sin (x + α) & \sin (x + β) & \sin (x + r) \\ \sin (β - r) & \sin (r - α) & \sin (α - β) \end{array}|, where x ε (0, \frac{π}{2}), α \neq β \neq r, then$

Difficult

A

$f (x) is negative if α, β, r are angels of acute angled triangle$
B

$f (x) is negative if α, β, r are angels of obtuse angled triangle$
C

$f (x) is negative if α, β, r are angels of right angled triangle$
D

$f (x) is strictly increasing function for every choice of α, β, r \in R$

Solution

$\begin{array}{l} f (x) = |\begin{array}{ccc} \cos x & - \sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{array}| \times |\begin{array}{ccc} \cos α & \sin α & \sin (β - r) \\ \cos β & \sin β & \sin (r - α) \\ \cos r & \sin r & \sin (α - β) \end{array}| \\ = - \{\sin^{2} (α - B) + \sin^{2} (β - r) + \sin^{2} (r - α)\} \end{array}$
$(o p e n t h e s e c o n d d e t e r m i n a n t a l o n g t h i r d c o l u m n)$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App