Pertanyaan

Diketahui sin p + sin q = 3 15 dan cos p + cos q = 3 15 , dengan dan q anggota bilangan real. Nilai dari sin ( p − q ) = ...

Diketahui $sin p + sin q = \frac{15}{3}$ dan $cos p + cos q = \frac{15}{3}$ , dengan $p$ dan $q$ anggota bilangan real. Nilai dari $sin (p - q) = ...$

L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

kedua ruas di kuadratkan kemudian buat segitiga siku-siku sehingga, . Jadi, jawaban yang tepat adalah D.

$sin p plus sin q equals fraction numerator square root of 15 over denominator 3 end fraction cos p plus cos q equals fraction numerator square root of 15 over denominator 3 end fraction$

kedua ruas di kuadratkan

$sin p plus sin q equals fraction numerator square root of 15 over denominator 3 end fraction space space space space space space rightwards arrow space sin squared p plus 2 sin p sin q plus sin squared q equals 15 over 9 bottom enclose cos p plus cos q equals fraction numerator square root of 15 over denominator 3 end fraction space space space space rightwards arrow cos squared p plus 2 cos p cos q plus cos squared q equals 15 over 9 space plus end enclose open parentheses sin squared p plus cos squared p close parentheses plus 2 open parentheses sin p sin q plus cos p cos q close parentheses space plus space open parentheses sin squared q plus space cos squared q close parentheses equals 30 over 9 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 1 plus 2 cos open parentheses p minus q close parentheses plus 1 equals 10 over 3 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 2 cos open parentheses p minus q close parentheses equals 10 over 3 minus 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 2 cos open parentheses p minus q close parentheses equals 4 over 3 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space cos open parentheses p minus q close parentheses equals 2 over 3$

kemudian buat segitiga siku-siku