Find the values of 7 sin 30° cos 60°

Find the values of

(i) 7 sin 30° cos 60°

(ii) 3 sin² 45° + 2 cos² 60°

(iii) cos² 45° + sin² 60° + sin² 30°

(iv) cos 90° + cos² 45° sin 30° tan 45°.

Answer :

(i) 7 sin 30° cos 60°

= 7 ×½ ×½

= (7×1×1)/(2×2)

= 7/4

(ii) 3 sin² 45° + 2 cos² 60°

= 3×(1/√2)² + [2×(1/2)²]

= (3×½) + (2 × ¼)

= 3/2 + ½

= (3 + 1)/2

= 4/2

= 2

(iii) cos² 45° + sin² 60° + sin² 30°

= (1/√2)² + (√3/2)² + (1/2)²

= ½ + ¾ + ¼

= (2 + 3 + 1)/4

= 6/4

= 3/2

(iv) cos 90° + cos² 45° sin 30° tan 45°

= 0 + (1/√2)² × ½ × 1

= ½ × ½ × 1

= ¼

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