Uji pemahaman materi invers trigonometri. Berapa hasil dari
[tex]\displaystyle \cos\left ( 2\arctan 3 \right )+\sin\left ( 2\arctan 3 \right )[/tex]
[tex]\displaystyle \cos\left ( 2\arctan 3 \right )+\sin\left ( 2\arctan 3 \right )[/tex]
Verified answer
JAWABAN
[tex]\displaystyle \sf\cos\left ( 2\arctan 3 \right )+\sin\left ( 2\arctan 3 \right ) = \: - \frac{1}{5} [/tex]
PEMBAHASAN
tan a = y/x = 3/1
r² = x² + y²
r² = 1² + 3²
r² = 10
tan a = 3
a = arctan 3
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cos (2 arctan 3)
= cos 2a
= cos² a - sin² a
= (x² - y²)/r²
= (1² - 3²)/10
= -4/5
sin (2 arctan 3)
= sin 2a
= 2 sin a cos a
= 2 × y/r × x/r
= 2 × 3 × 1/10
= 3/5
cos (2 arctan 3) + sin (2 arctan 3)
= -4/5 + 3/5
= -1/5