Verify each of the following :
(i) sin 60° cos 30° - cos 60° sin 30° = sin 30°
(ii) 2 sin 30° cos 30° = sin 60°
(iii) 2 sin 45° cos 45° = sin 90°

Question

Verify each of the following : (i) sin 60 cos 30 - cos 60 sin 30 = sin 30 (ii) 2 sin 30 cos 30 = sin 60 (iii) 2 sin 45 cos 45 = sin 90

KnowledgeBoat · Accepted Answer

(i) Left Hand Side : sin 60 cos 30 - cos 60 sin 30 = = = . Right Hand Side : sin 30 = Hence, proved that sin 60 cos 30 - cos 60 sin 30 = sin 30 . (ii) Left Hand Side : 2 sin 30 cos 30 = = Right Hand Side : sin 60 = Hence, proved that 2 sin 30 cos 30 = sin 60 . (iii) Left Hand Side : 2 sin 45 cos 45 = = 1 Right Hand Side : sin 90 = 1 Hence, proved that 2 sin 45 cos 45 = sin 90 .

Mathematics

Verify each of the following :
(i) sin 60° cos 30° - cos 60° sin 30° = sin 30°
(ii) 2 sin 30° cos 30° = sin 60°
(iii) 2 sin 45° cos 45° = sin 90°

Trigonometrical Ratios

Related Questions

If A = 45°, verify that :
(i) sin 2A = 2 sin A cos A
(ii) cos 2A = (2 cos²A - 1) = (1 - 2 sin²A)

Mathematics

Verify each of the following :(i) sin 60° cos 30° - cos 60° sin 30° = sin 30°(ii) 2 sin 30° cos 30° = sin 60°(iii) 2 sin 45° cos 45° = sin 90°

Trigonometrical Ratios

Related Questions

If A = 45°, verify that :(i) sin 2A = 2 sin A cos A(ii) cos 2A = (2 cos2A - 1) = (1 - 2 sin2A)

Verify each of the following :
(i) sin 60° cos 30° - cos 60° sin 30° = sin 30°
(ii) 2 sin 30° cos 30° = sin 60°
(iii) 2 sin 45° cos 45° = sin 90°

If A = 45°, verify that :
(i) sin 2A = 2 sin A cos A
(ii) cos 2A = (2 cos²A - 1) = (1 - 2 sin²A)