Diketahui Alfa(a)=45° dan Beta(b)= 60°,Hitung! 1. 2 × sin 45° × cos 60° 2. sin 45° × cos 60° + sin 60° × cos 45 ° 3. sin 45° × cos 60° - sin 60° × cos 45° 4. tan 45° + tan 60° /1(tan 45° × tan 60°) 5. sin²45° + cos²60° +sin²60° + cos²45° kalau soal tidak jelas silakan lihat foto,bantuin Aku yg masih junior kak
Answer (2)
(( − 2 ) 2 − 4 ) 3 + 4 ⋅ ( − 5 ) = ( 4 − 4 ) 3 + ( − 20 ) = 0 3 − 20 = 0 − 20 = − 20
Jawab:[tex]1.\sin(\alpha + \beta) + \sin(\alpha - \beta)\\2.\sin(\alpha + \beta)\\3.\sin(\alpha - \beta)\\4.\cot \beta + \cot \alpha\\5.2$[/tex]Penjelasan dengan langkah-langkah:Diketahui:[tex]\alpha = 45^\circ[/tex][tex]\beta = 60^\circ[/tex]Jawab:1.[tex]2 \cdot \sin \alpha \cdot \cos \beta[/tex]Gunakan identitas:[tex]2 \sin A \cos B = \sin(A + B) + \sin(A - B)[/tex][tex]\Rightarrow 2 \sin \alpha \cos \beta = \sin(\alpha + \beta) + \sin(\alpha - \beta)[/tex][tex]= \boxed{ \sin(\alpha + \beta) + \sin(\alpha - \beta) }[/tex]2.[tex]\sin \alpha \cos \beta + \sin \beta \cos \alpha[/tex]Gunakan identitas:[tex]\sin A \cos B + \sin B \cos A = \sin(A + B)[/tex] [tex]\Rightarrow \boxed{ \sin(\alpha + \beta) }[/tex]3.[tex]\sin \alpha \cos \beta - \sin \beta \cos \alpha[/tex]Gunakan identitas:[tex]\sin A \cos B - \sin B \cos A = \sin(A - B)[/tex] [tex]\Rightarrow \boxed{ \sin(\alpha - \beta) }[/tex]4.[tex]\frac{ \tan \alpha + \tan \beta }{ \tan \alpha \cdot \tan \beta }[/tex]Pisahkan pecahan:[tex]= \frac{ \tan \alpha }{ \tan \alpha \cdot \tan \beta } + \frac{ \tan \beta }{ \tan \alpha \cdot \tan \beta }[/tex][tex]= \frac{1}{ \tan \beta } + \frac{1}{ \tan \alpha }[/tex][tex]= \boxed{ \frac{1}{\tan \beta} + \frac{1}{\tan \alpha} }\quad \text{(atau: } \boxed{ \cot \beta + \cot \alpha } \text{)}[/tex]5.[tex]\sin^2 \alpha + \cos^2 \beta + \sin^2 \beta + \cos^2 \alpha[/tex]Kelompokkan:[tex]= (\sin^2 \alpha + \cos^2 \alpha) + (\sin^2 \beta + \cos^2 \beta)[/tex]Gunakan identitas:[tex]\sin^2 x + \cos^2 x = 1[/tex][tex]= 1 + 1 = \boxed{2}[/tex]
