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

Question

KnowledgeBoat · Accepted Answer

(i) L.H.S. : sin 2A = sin 2(45 ) = sin 90 = 1 R.H.S. : 2 sin A cos A = 2 sin 45 cos 45 = = 1. Hence, proved that sin 2A = 2 sin A cos A. (ii) Substituting value of A = 45 in cos 2A, we get : cos 2A = cos 2(45 ) = cos 90 = 0. Substituting value of A = 45 in 2 cos2A - 1, we get : ⇒ 2 cos2A - 1 = 2 cos245 - 1 = 2 (cos 45 )2 - 1 = - 1 = = 1 - 1 = 0. Substituting value of A = 45 in 1 - 2 sin2A, we get : ⇒ 1 - 2 sin2A = 1 - 2 sin245 = 1 - 2 (sin 45 )2 = 1 - = 1 - = 1 - 1 = 0. Hence, proved that cos 2A = (2 cos2A - 1) = (1 - 2 sin2A).

Mathematics

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

Trigonometrical Ratios

Related Questions

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 = B = 45°, show that :
(i) sin(A - B) = sin A cos B - cos A sin B
(ii) cos(A + B) = cosA cosB - sin A sin B

Mathematics

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

Trigonometrical Ratios

Related Questions

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 = B = 45°, show that :(i) sin(A - B) = sin A cos B - cos A sin B(ii) cos(A + B) = cosA cosB - sin A sin B

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 = B = 45°, show that :
(i) sin(A - B) = sin A cos B - cos A sin B
(ii) cos(A + B) = cosA cosB - sin A sin B