Reduce the following to the sine or cosine of one angle:

Question

(i) sin145*cos75 - cos145*sin75
(ii) cos35*cos15 - sin35*sin15

Use the formulae:

sin(a+b)= sin(a) cos(b) + cos(a)sin(b)

and

cos(a+b)= cos(a)cos(b) - sin(a)sin)(b)

(1)The quantity = sin(145-75)
= sin 70
= cos 20
note that If a+b=90 degrees then
sin a = cos b
(2) The quantity = cos (35 + 15)
= cos 50
= sin 40