Boleh minta tolong ….., bantuin yaaa

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Boleh minta tolong …..
bantuin yaaa​

 

3)

\tan( \alpha + \beta ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{1 - \tan( \alpha ) \tan( \beta ) } \\ = \frac{ \frac{1}{2} + \frac{1}{3} }{1 - \frac{1}{2}( \frac{1}{3} ) } \\ = \frac{ \frac{3 + 2}{6} }{ \frac{6 - 1}{6} } \\ = \frac{ \frac{5}{6} }{ \frac{5}{6} } = \frac{5}{6} \times \frac{6}{5} = 1

4a)

\sin(45 + \alpha ) - \sin(45 - \alpha ) \\ = ( \sin(45) \cos( \alpha ) + \sin( \alpha ) \cos(45) ) - ( \sin(45) \cos( \alpha ) - \cos(45) \sin( \alpha ) ) \\ = \sin( \alpha ) \cos(45) + \sin( \alpha ) \cos(45) \\ = 2 \sin( \alpha ) \cos(45) \\ = 2 \sin( \alpha ) ( \frac{1}{2} \sqrt{2} ) \\ = \sqrt{2} \sin( \alpha )

terbukti

b)

\sin(150 + \alpha ) + \sin(30 + \alpha ) \\ = (\sin(150) \cos( \alpha ) + \cos( 150 ) \sin( \alpha ) ) + ( \sin(30) \cos( \alpha ) + \sin( \alpha ) \cos(30) )

dimana

sin 30 = sin 150

cos 150 = -cos 30

= (\sin(30) \cos( \alpha ) - \cos( 30 ) \sin( \alpha ) ) + ( \sin(30) \cos( \alpha ) + \sin( \alpha ) \cos(30) ) \\ = 2 \sin(30) \cos( \alpha ) \\ = 2( \frac{1}{2} ) \cos( \alpha ) \\ = \cos( \alpha )

terbukti

5)

\sin(c) = \frac{y}{r} = \frac{3}{5}

x = \sqrt{ {5}^{2} - {3}^{2} } \\ = \sqrt{25 - 9} \\ = \sqrt{16} = 4

maka

\tan(c) = \frac{y}{x} = \frac{3}{4}

a)

jumlah sudut segitiga = 180

a+b+c = 180

\tan(a + b) = \tan(180 - c) \\ = - \tan(c) \\ = - \frac{3}{4}

b)

\tan(a + b) = \frac{ \tan(a) + \tan(b) }{1 - \tan(a) \tan(b) } \\ \tan(a) + \tan(b) = \tan(a + b) (1 - \tan(a) \tan(b) ) \\ = - \frac{3}{4} (1 - 5) \\ = - \frac{3}{4} ( - 4) \\ = 3

maaf cuma bantu itu ja

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