Question

Please explain your answer. THX!!!

Answer 1

Answer:

1) cos (3x)

2) $\frac{-(1-\sqrt{3})^{2}}{2}$

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) = $\sqrt{\frac{1 - cos(x)}{1+cos(x)} }$

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

cos π/6 = $\frac{\sqrt{3} }{2}$

= -$\sqrt{\frac{1-\frac{\sqrt{3} }{2} }{1+\frac{\sqrt{3} }{2} } }$

= - $\sqrt{7-4\sqrt{3} }$

= - 2+$\sqrt{3}$

= $-\frac{(1-\sqrt{3}) ^{2} }{2}$

!