Answer:
see explanation
Step-by-step explanation:
(3)
Given cosΘ = - [tex]\frac{4}{5}[/tex]
Then by Pythagoras' theorem the third side is 3 ( 3,4, 5 triangle )
Since Θ in second quadrant then sinΘ > 0
sinΘ = [tex]\frac{3}{5}[/tex]
Using the trigonometric identity
sin2Θ = 2sinΘcosΘ, then
sin2Θ = 2 × [tex]\frac{3}{5}[/tex] × - [tex]\frac{4}{5}[/tex] = - [tex]\frac{24}{25}[/tex]
(4)
Using the trigonometric identity
cos(x - y) = cosxcosy + sinxsiny
note cos15° = cos(45 - 30)°
cos(45 - 30) = cos45cos30 + sin45sin30
= ( [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex]) + ([tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{1}{2}[/tex])
= [tex]\frac{\sqrt{2(\sqrt{3}+1) } }{4}[/tex]
