Question

Evaluate:

`[(cos 45°, sin 30°),(sqrt(2) cos 0°, sin 0°)] [(sin 45°, cos 90°),(sin 90°, cot 45°)]`

Answer 1

`[(cos 45°, sin 30°),(sqrt(2) cos 0°, sin 0°)] [(sin 45°, cos 90°),(sin 90°, cot 45°)]`

We know that:

cos 45° = `1/sqrt(2)`, sin 30° = `1/2`, sin 45° = `1/sqrt(2)`

cos 90° = 0, cos 0° = 1, sin 90° = 1, cot 45° = 1

= `[(1/sqrt(2), 1/2),(sqrt(2) xx 1, 0)][(1/sqrt(2), 0),(1, 1)]`

= `[(1/sqrt(2) xx 1/sqrt(2) + 1/2 xx 1, 1/sqrt(2) xx 0 + 1/2 xx 1),(sqrt(2) xx 1/sqrt(2) + 0 xx 1, sqrt(2) xx 0 + 0 xx 1)]`

= `[(1/2+ 1/2, 0 + 1/2),(1 + 0, 0 + 0)]`

= `[(1, 1/2),(1, 0)]`

= `[(1, 0.5),(1, 0)]`