Question

02. Prove that
(a) sin 420° cos 390° + cos(-300°) sin(-330°) = 1​

Answer 1

Answer:

sin 420 can be written as sin(360+60)=sin 60

cos 390=cos(360+30)=cos 30

cos(-300)=cos300=cos(360-60)=cos60

sin(-330)=-sin(360-30)=-(-sin(30)) because fourth quadrant so sin negative

=sin30

now sin60 cos30+cos60sin30

this is like sin(A+B)= sin a cos b+ cos a sin b

sin(60+30)=sin90=1