Evaluate the following determinant: cos 90 ° - cos 45 ° sin 90 ° sin 45 ° .

Given that, ∆ = cos 90 ° - cos 45 ° sin 90 ° sin 45 ° We have to find the value of ∆ . cos 90 ° - cos 45 ° sin 90 ° sin 45 ° = 0 - 1 2 1 1 2 [ ∵ cos 90 ° = 0 , cos 45 ° = 1 2 , sin 90 ° = 1 , sin 45 ° = 1 2 ] Using definition of expansion of determinant, we get = 0 1 2 - - 1 2 1 = 0 + 1 2 = 1 2 .

Evaluate the following determinant: cos 90 ° - cos 45 ° sin 90 ° sin 45 ° .

Given that, ∆ = cos 90 ° - cos 45 ° sin 90 ° sin 45 ° We have to find the value of ∆ . cos 90 ° - cos 45 ° sin 90 ° sin 45 ° = 0 - 1 2 1 1 2 [ ∵ cos 90 ° = 0 , cos 45 ° = 1 2 , sin 90 ° = 1 , sin 45 ° = 1 2 ] Using definition of expansion of determinant, we get = 0 1 2 - - 1 2 1 = 0 + 1 2 = 1 2 .

Find the value of x if x 4 2 2 x = 0 .

We have to find the value of x . Given equation is x 4 2 2 x = 0 Expanding the determinant, ⇒ ( x × 2 x ) - ( 4 × 2 ) = 0 [ ∵ ∆ = a 1 a 2 b 1 b 2 = a 1 b 2 - a 2 b 1 ] ⇒ 2 x 2 - 8 = 0 ⇒ 2 x 2 = 8 ⇒ x 2 = 8 2 ⇒ x 2 = 4 ⇒ x = ± 4 ⇒ x = ± 2 Hence, value of x are 2 and - 2 .