Pertanyaan

Bentuk sederhana dari sin A + cos A tan A − sin A − cos A tan A adalah ....

Bentuk sederhana dari $\frac{tan A}{sin A + cos A} - \frac{tan A}{sin A - cos A}$ adalah ....

−2 sin A sec 2A
−2 cos A csc 2A
2 csc A sec 2A
2 sin A sec 2A
2 cos A csc 2A

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Klaim

M. Robo

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan bahwa Jadi, jawaban yang tepat adalah D.

Perhatikan bahwa

$begin mathsize 14px style fraction numerator tan invisible function application A over denominator sin invisible function application A plus cos invisible function application A end fraction minus fraction numerator tan invisible function application A over denominator sin invisible function application A minus cos invisible function application A end fraction equals fraction numerator tan invisible function application A open parentheses sin invisible function application A minus cos invisible function application A close parentheses over denominator open parentheses sin invisible function application A plus cos invisible function application A close parentheses open parentheses sin invisible function application A minus cos invisible function application A close parentheses end fraction minus fraction numerator tan invisible function application A open parentheses sin invisible function application A plus cos invisible function application A close parentheses over denominator open parentheses sin invisible function application A plus cos invisible function application A close parentheses open parentheses sin invisible function application A minus cos invisible function application A close parentheses end fraction equals fraction numerator tan invisible function application A sin invisible function application A minus tan invisible function application A cos invisible function application A over denominator sin squared invisible function application A minus cos squared invisible function application A end fraction minus fraction numerator tan invisible function application A sin invisible function application A plus tan invisible function application A cos invisible function application A over denominator sin squared invisible function application A minus cos squared invisible function application A end fraction equals fraction numerator open parentheses tan invisible function application A sin invisible function application A minus tan invisible function application A cos invisible function application A close parentheses minus open parentheses tan invisible function application A sin invisible function application A plus tan invisible function application A cos invisible function application A close parentheses over denominator sin squared invisible function application A minus cos squared invisible function application A end fraction equals fraction numerator tan invisible function application A sin invisible function application A minus tan invisible function application A cos invisible function application A minus tan invisible function application A sin invisible function application A minus tan invisible function application A cos invisible function application A over denominator sin squared invisible function application A minus cos squared invisible function application A end fraction equals fraction numerator negative 2 tan invisible function application A cos invisible function application A over denominator sin squared invisible function application A minus cos squared invisible function application A end fraction equals fraction numerator negative 2 tan invisible function application A cos invisible function application A over denominator negative open parentheses negative sin squared invisible function application A plus cos squared invisible function application A close parentheses end fraction equals fraction numerator 2 tan invisible function application A cos invisible function application A over denominator cos squared invisible function application A minus sin squared invisible function application A end fraction equals fraction numerator 2 times fraction numerator sin invisible function application A over denominator cos invisible function application A end fraction times cos invisible function application A over denominator cos invisible function application 2 A end fraction equals fraction numerator 2 sin invisible function application A over denominator cos invisible function application 2 A end fraction equals 2 sin invisible function application A sec invisible function application 2 A end style$

Jadi, jawaban yang tepat adalah D.