Jawab:
Penjelasan dengan langkah-langkah:
18. tan x = - R
maka kita dapat menggunakan rumus 1 + tan ² x = sec ² x
1 + R² = sec ² x
karena cos ² x = [tex]\frac{1}{sec^{2}x }[/tex] = [tex]\frac{1}{1 + R^{2} }[/tex]
Cos 2x = 2 cos ² x - 1 = [tex]\frac{2}{1 + R^{2} }[/tex] - 1 = [tex]\frac{1 - R^{2} }{1 + R^{2} }[/tex]
19. tan ( P + 50 ) = m
tan ( P + 5 + 45 ) = m
tan ( ( P + 5 ) + 45 ) = m gunakan rumus
tan ( A + B ) = ( tan A + tan B ) / ( 1 - tan A . tan B )
tan ( ( P + 5 ) + 45 ) = ( tan ( P + 5 ) + tan 45 )/ ( 1 - tan ( P + 5 ) . tan 45 )
= ( tan ( P + 5 ) + 1 ) / ( 1 - tan ( P + 5 ) ) = m
( tan ( P + 5 ) + 1 ) / ( 1 - tan ( P + 5 ) ) = m
Misalkan tan ( P + 5 ) = x
( x + 1 ) / ( 1 - x ) = m
atau
x = ( m - 1 ) / ( m + 1 )
karena tan ( P + 5 ) = x
tan ( P + 5 ) = ( m - 1 ) / ( m + 1 )
20. cos 50 . cos 70 - sin 50 . sin 70 = cos ( 50 + 70 )
= cos 120
= -1/2
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