Question

Find the value of x in the following: i) cos x = cos60° cos30° + cos60° sin30° , ii) sin2x = sin60° cos30° - cos60° sin30° ,iii) √3tan2x = sin30° +sin45° cos45°+2sin90°

Answer 1

$\cos(60) = 1 \div 2$
$\cos(30) = \sqrt{3} \div 2$

Answer 2

i)cosx=(1/2)(√3/2)+1/2(1/2)=√3+1/4 i.e. x=cos^-1(0.683)
ii)sinAcosB-cosAsinB=sin(A-B) so sin2x=sin(60-30)= sin30 x=15 degrees
iii) √3 tan2x= 1/2+(1/√2)(1/√2)+2 = 3. tan2x =3/√3= √3. tan2x=tan60 . x=30 degrees