Answer:
1) cos (3x)
2) [tex]\frac{-(1-\sqrt{3})^{2}}{2}[/tex]
Step-by-step explanation:
Given expression:
cos(7x)cos(4x)+sin(7x)sin(4x)
By using the trigonometric identity
cos(a)cos(b) + sin(a)sin(b) = cos(a-b)
we have:
cos(7x)cos(4x)+sin(7x)sin(4x) = cos(7x - 4x)
= cos(3x)!
part 2:
tan (-π/12)
by using property tan(-x)= - tan(x)
=-tan(π/12)
= - tan(π/6 / 2)
Using tan(x/2) = [tex]\sqrt{\frac{1 - cos(x)}{1+cos(x)} }[/tex]
= - [tex]\sqrt{\frac{1 - cos(pi/6)}{1+cos(pi/6)} }[/tex]
cos π/6 = [tex]\frac{\sqrt{3} }{2}[/tex]
= -[tex]\sqrt{\frac{1-\frac{\sqrt{3} }{2} }{1+\frac{\sqrt{3} }{2} } }[/tex]
= - [tex]\sqrt{7-4\sqrt{3} }[/tex]
= - 2+[tex]\sqrt{3}[/tex]
= [tex]-\frac{(1-\sqrt{3}) ^{2} }{2}[/tex]
!
