Question

Please explain your answer. THX!!!

Answer 1

1) cos (3x)

2)
`(-(1-√(3))^(2))/(2)`

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) =
`\sqrt{(1 - cos(x))/(1+cos(x)) }`

= -
`\sqrt{(1 - cos(pi/6))/(1+cos(pi/6)) }`

cos π/6 =
`(√(3) )/(2)`

= -
`\sqrt{(1-(√(3) )/(2) )/(1+(√(3) )/(2) ) }`

= -
`\sqrt{7-4√(3) }`

= - 2+
`√(3)`

=
`-((1-√(3)) ^(2) )/(2)`

!