Q27 of 186 Page 350

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

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

If tan²45° – cos²30° = x sin 45° cos 45° then x = ?

sec²60° – 1 = ?

sin² 30° + 4 cot² 45° – sec² 60° = ?

3 cos²60° + 2 cot²30° – 5 sin²45° = ?