Answer:
sin2x = [tex]\frac{30}{34}[/tex]
Step-by-step explanation:
Given
tanx = [tex]\frac{3}{5}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]
This is a right triangle with legs 3 and 5
Let the hypotenuse be h , then using Pythagoras' identity
h² = 3² + 5² = 9 + 25 = 34 ( take the square root of both sides )
h = [tex]\sqrt{34}[/tex]
Thus
sinx = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{\sqrt{34} }[/tex]
cosx = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{5}{\sqrt{34} }[/tex]
Hence
sin2x = 2sinxcosx = 2 × [tex]\frac{3}{\sqrt{34} }[/tex] × [tex]\frac{5}{\sqrt{34} }[/tex] = [tex]\frac{2(3)(5)}{\sqrt{34}(\sqrt{34}) }[/tex] = [tex]\frac{30}{34}[/tex]
