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Jawablah pertanyaan-pertanyan di bawah ini dengan ...

Jawablah pertanyaan-pertanyan di bawah ini dengan benar!

Buktikan Identitas-identitas trigonometri berikut!

begin mathsize 14px style fraction numerator sin x over denominator 1 plus cos x end fraction plus fraction numerator 1 plus cos x over denominator sin x end fraction equals 2 cos e c x end style

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Jawaban:

Akan dibuktikan begin mathsize 14px style fraction numerator sin x over denominator 1 plus cos x end fraction plus fraction numerator 1 plus cos x over denominator sin x end fraction equals 2 cos e c x end style

Ingat Bahwa begin mathsize 14px style sin squared x plus cos squared x equals 1 end style begin mathsize 14px style semicolon cosec x equals fraction numerator 1 over denominator sin x end fraction end style.

begin mathsize 14px style rightwards arrow fraction numerator sin x over denominator 1 plus cos x end fraction plus fraction numerator 1 plus cos x over denominator sin x end fraction equals fraction numerator sin squared x plus left parenthesis 1 plus cos x right parenthesis squared over denominator open parentheses 1 plus cos x close parentheses sin x end fraction equals fraction numerator sin squared x plus 1 plus 2 cos x plus cos squared x over denominator open parentheses 1 plus cos x close parentheses sin x end fraction equals fraction numerator sin squared x plus cos squared x plus 1 plus 2 cos x over denominator open parentheses 1 plus cos x close parentheses sin x end fraction equals fraction numerator 1 plus 1 plus 2 cos x over denominator open parentheses 1 plus cos x close parentheses sin x end fraction equals fraction numerator 2 plus 2 cos x over denominator open parentheses 1 plus cos x close parentheses sin x end fraction equals fraction numerator 2 left parenthesis 1 plus cos x right parenthesis over denominator open parentheses 1 plus cos x close parentheses sin x end fraction equals fraction numerator 2 over denominator sin x end fraction equals 2 cosec x end style

Jadi, terbukti bahwa 

begin mathsize 14px style fraction numerator sin x over denominator 1 plus cos x end fraction plus fraction numerator 1 plus cos x over denominator sin x end fraction equals 2 cos e c x end style

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