If A = 60 and B = 30 , show that : (sin A cos B + cos A sin B)2 + (cos A cos B - sin A sin B)2 = 1

Question

KnowledgeBoat · Accepted Answer

Left Hand Side : (sin A cos B + cos A sin B)2 + (cos A cos B - sin A sin B)2 = (sin 60 cos 30 + cos 60 sin 30 )2 + (cos 60 cos 30 - sin 60 sin 30 )2 = = = 1 + 0 = 1. Right Hand Side = 1 Hence, proved that (sin A cos B + cos A sin B)2 + (cos A cos B - sin A sin B)2 = 1.

Mathematics

If A = 60° and B = 30°, show that :
(sin A cos B + cos A sin B)² + (cos A cos B - sin A sin B)² = 1

Trigonometrical Ratios

Related Questions

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 = 60° and B = 30°, show that :(sin A cos B + cos A sin B)2 + (cos A cos B - sin A sin B)2 = 1

Trigonometrical Ratios

Related Questions

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 = 60° and B = 30°, show that :
(sin A cos B + cos A sin B)² + (cos A cos B - sin A sin B)² = 1

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