Question

Value of the determinant `[(cos67°,sin67°),(sin23°,cos23°)]` is ______.

Options

• 0

• `1/2`

• `sqrt(3)/2`

• 1

Answer 1

Value of the determinant `[(cos67°,sin67°),(sin23°,cos23°)]` is 0.

Explanation:

`[(cos67°,sin67°),(sin23°,cos23°)]`

= cos 67° cos 23° – sin 67° sin 23°

= cos (67° + 23°)  ...[Using cos (A + B) = cos A cos B – sin A sin B]

= cos 90°

= 0