Pertanyaan

Jika tan α = 1 dan tan β = 3 1 dengan α dan β sudut lancip, maka sin ( α − β ) = ...

Jika $tan α = 1$ dan $tan β = \frac{1}{3}$ dengan $α$ dan $β$ sudut lancip, maka $sin (α - β)$ = ...

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Nilai dengan sudut lancip

$tan space open parentheses alpha minus beta close parentheses equals fraction numerator tan alpha minus tan beta over denominator 1 plus tan alpha space tan beta end fraction space space space space space space space space space space space space space space space equals fraction numerator 1 minus begin display style 1 third end style over denominator 1 plus left parenthesis 1 right parenthesis open parentheses begin display style 1 third end style close parentheses end fraction equals fraction numerator begin display style 2 over 3 end style over denominator begin display style 4 over 3 end style end fraction equals 1 half$

$sin space left parenthesis alpha minus beta right parenthesis equals fraction numerator 1 over denominator square root of 5 end fraction cross times fraction numerator square root of 5 over denominator square root of 5 end fraction equals fraction numerator 1 over denominator square root of 5 end fraction square root of 5$