Sederhanakan bentuk sin 52° sin 68° + sin 47°cos 77° - cos 65° cos 81°

Halo Nasywa, kakak bantu jawab ya. Bentuk sederhananya adalah cos 34°. Konsep: sin A sin B = -(1/2)[cos(A+B) - cos (A-B)] sin A cos B = (1/2)[sin (A+B) + sin (A-B)] cos A cos B = (1/2)[cos (A+B) + cos (A-B)] Pembahasan: sin 52° sin 68° + sin 47°cos 77° - cos 65° cos 81° = [-(1/2)[cos(52°+68°) - cos (52°-68°)]+[(1/2)[sin (47°+77°) + sin (47°-77°)]-(1/2)[cos (65°+81°) + cos (65°-81°)] =[-(1/2)[cos 120° - cos (-16°)] + (1/2)[sin 124° + sin (-30°)] - (1/2) [ cos 146° + cos (-16°)] =[-(1/2)[(-1/2) - cos (16°)] + (1/2)[sin 124° + (-1/2)] - (1/2) [ cos 146° + cos (16°)] =[(1/4) + (1/2)cos 16° + (1/2)sin 124° - (1/4) - (1/2) cos 146° - (1/2)cos 16° =(1/2)(sin 124°-cos 146°) =(1/2)(sin 124Halo Nasywa, kakak bantu jawab ya. Konsep: sin A sin B = -(1/2)[cos(A+B) - cos (A-B)] sin A cos B = (1/2)[sin (A+B) + sin (A-B)] cos A cos B = (1/2)[cos (A+B) + cos (A-B)] cos (90°+a) = - sin a sin A + sin B = 2 sin ((A+B)/2) cos ((A-B)/2) Pembahasan: sin 52° sin 68° + sin 47°cos 77° - cos 65° cos 81° = [-(1/2)[cos(52°+68°) - cos (52°-68°)]+[(1/2)[sin (47°+77°) + sin (47°-77°)]-(1/2)[cos (65°+81°) + cos (65°-81°)] =[-(1/2)[cos 120° - cos (-16°)] + (1/2)[sin 124° + sin (-30°)] - (1/2) [ cos 146° + cos (-16°)] =[-(1/2)[(-1/2) - cos (16°)] + (1/2)[sin 124° + (-1/2)] - (1/2) [ cos 146° + cos (16°)] =[(1/4) + (1/2)cos 16° + (1/2)sin 124° - (1/4) - (1/2) cos 146° - (1/2)cos 16° =(1/2)(sin 124°-cos 146°) =(1/2)( sin 124°- cos (90°+56°)) =(1/2) (sin 124° -(-sin 56°) =(1/2)(sin 124° + sin 56°) =(1/2)[2 sin ((124°+56°)/2) cos ((124°-56°)/2)] =(1/2)[2 sin 90° cos 34°] =sin 90° cos 34° = 1 (cos 34°) = cos 34° Jadi, bentuk sederhananya adalah cos 34°. Semoga membantu ya.