Question

PLEASE HELP ME!!! I don’t understand

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the addition formula for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

and exact values

sin45° = cos45° = $\frac{\sqrt{2} }{2}$

c0s30° = $\frac{\sqrt{3} }{2}$ , sin30° = $\frac{1}{2}$

Express cos15° = cos(45 - 30 )°, then

cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

= $\frac{\sqrt{2} }{2}$ × $\frac{\sqrt{3} }{2}$ + ( $\frac{\sqrt{2} }{2}$ × $\frac{1}{2}$ )

= $\frac{\sqrt{6} }{4}$ + $\frac{\sqrt{2} }{4}$

= $\frac{\sqrt{6}+\sqrt{2} }{4}$ ← exact value

Answer 2

Answer:

   √6 + √2

= --------------

        4

Step-by-step explanation:

15° = 45° - 30°

So

cos(15)  = cos(45 - 30)

=cos(45)  × cos(30) + sin(45) × sin(30)

= 1/√2  × (√3)/2  + 1/√2 × 1/2

    (√3) + 1

= --------------

     2√2

    (√3) + 1              √2

= -------------- x       ---------

     2√2                  √2

   √6 + √2

= --------------

        4