Evaluate |(cos 15°, sin 15°),(sin 75°, cos 75°)|

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Asked: 2023-11-01T11:07:24+05:30 In: Mathematics
Evaluate |(cos 15°, sin 15°),(sin 75°, cos 75°)|

Hi, I have a question and I hope anyone could answer it:

Evaluate (begin{vmatrix} cos 15^circ &sin 15^circ\[0.3em] sin 75^circ & cos 75^circ \[0.3em] end{vmatrix}) 

Evaluate |(cos 15°, sin 15°),(sin 75°, cos 75°)|

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    1 Answer

    2. Expanding the determinant, we get 

      cos 15° . cos 75° – sin 15° . sin 75° 

      = cos (15° + 75° ) = cos 90° = 0

      [since cos (A + B) = cos A. cos B – sinA . sin B]

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