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Buktikanlah setiap identitas trigonometri berikut ini. ( tan α + sin α ) ( 1 − cos α ) = sin 2 α tan α

Buktikanlah setiap identitas trigonometri berikut ini.

$(tan α + sin α) (1 - cos α) = sin^{2} α tan α$

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

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Terbukti.

$table attributes columnalign right center left columnspacing 2px end attributes row cell begin mathsize 14px style left parenthesis tan space alpha plus sin space alpha right parenthesis end style begin mathsize 14px style left parenthesis 1 minus cos space alpha right parenthesis end style end cell size 14px equals cell size 14px sin to the power of size 14px 2 size 14px space size 14px alpha size 14px space size 14px tan size 14px space size 14px alpha end cell row cell begin mathsize 14px style left parenthesis fraction numerator sin space alpha over denominator cos space alpha end fraction plus sin space alpha right parenthesis end style begin mathsize 14px style left parenthesis 1 minus cos space alpha right parenthesis end style end cell size 14px equals cell size 14px sin to the power of size 14px 2 size 14px space size 14px alpha size 14px space size 14px tan size 14px space size 14px alpha end cell row cell size 14px sin size 14px space size 14px alpha size 14px space begin mathsize 14px style left parenthesis fraction numerator 1 plus cos space alpha over denominator cos space alpha end fraction right parenthesis end style begin mathsize 14px style left parenthesis 1 minus cos space alpha right parenthesis end style end cell size 14px equals cell size 14px sin to the power of size 14px 2 size 14px space size 14px alpha size 14px space size 14px tan size 14px space size 14px alpha end cell row cell size 14px sin size 14px space size 14px alpha size 14px space begin mathsize 14px style left parenthesis fraction numerator 1 minus cos squared space alpha over denominator cos space alpha end fraction right parenthesis end style end cell size 14px equals cell size 14px sin to the power of size 14px 2 size 14px space size 14px alpha size 14px space size 14px tan size 14px space size 14px alpha end cell row cell fraction numerator size 14px sin size 14px space size 14px alpha over denominator size 14px cos size 14px space size 14px alpha end fraction begin mathsize 14px style left parenthesis 1 minus cos squared space alpha right parenthesis end style end cell size 14px equals cell size 14px sin to the power of size 14px 2 size 14px space size 14px alpha size 14px space size 14px tan size 14px space size 14px alpha end cell row cell size 14px sin to the power of size 14px 2 size 14px space size 14px alpha size 14px space size 14px tan size 14px space size 14px alpha end cell size 14px equals cell size 14px sin to the power of size 14px 2 size 14px space size 14px alpha size 14px space size 14px tan size 14px space size 14px alpha end cell end table$

Terbukti.