Question

If 2cos 2x =
$\sqrt{3}$
and x is acute angle, find:
(i) sin 3x (ii) * (iii) cos2 (45° + x) + sin2 (75° - x)​

Answer 1

Answer:

cos 2x=√3/2

cos 30=√3/2

30=2x

x=15

1) sin3(15) =sin45=1/√2

3) cos2(45+15) =cos120=cos(90-(-30)) =sin(-30) =-sin30=-1/2

sin2(75-15)

sin120=sin(90-(-30)) =cos(-30) =cos30=√3/2

cos120+sin120=-1/2+√3/2

(√3-1) /2