# trig

posted by
**Paul C**
.

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

(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