Prove that sin 80 ° cos 20 ° - cos 80 ° sin 20 ° = 3 2 .

To prove that sin 80 ° cos 20 ° - cos 80 ° sin 20 ° = 3 2 . We know that sin A cos B - cos A sin B = sin A - B . Now, sin 80 ° cos 20 ° - cos 80 ° sin 20 ° = sin 80 ° - 20 ° = sin 60 ° = 3 2 Hence, proved that sin 80 ° cos 20 ° - cos 80 ° sin 20 ° = 3 2 .

Prove that cos 45 ° cos 15 ° - sin 45 ° sin 15 ° = 1 2 .

To prove that cos 45 ° cos 15 ° - sin 45 ° sin 15 ° = 1 2 . We know that cos A cos B - sin A sin B = cos A + B . Now, cos 45 ° cos 15 ° - sin 45 ° sin 15 ° = cos 45 ° + 15 ° = cos 60 ° = 1 2 Hence, proved that cos 45 ° cos 15 ° - sin 45 ° sin 15 ° = 1 2 .

Prove that cos 75 ° cos 15 ° + sin 75 ° sin 15 ° = 1 2 .

To prove that cos 75 ° cos 15 ° + sin 75 ° sin 15 ° = 1 2 . We know that cos A cos B + sin A sin B = cos A - B . Now, cos 75 ° cos 15 ° + sin 75 ° sin 15 ° = cos 75 ° - 15 ° = cos 60 ° = 1 2 Hence, proved that cos 75 ° cos 15 ° + sin 75 ° sin 15 ° = 1 2 .