(cos 0° + sin 30° + sin 45°) (sin 90° + cos 60° – cos 45°) = ?

Question

Philoid · Accepted Answer

Consider (cos 0° + sin 30° + sin 45°) (sin 90° + cos 60° – cos 45°)

= [1 + (1/2) + (1/√2)] × [1 + (1/2) – (1/√2)]

= [(3/2) + (1/√2)] × [(3/2) – (1/√2)]

= (3/2)² – (1/√2)²

= (9/4) – (1/2)

= (9 – 2)/4

= 7/4