TRIG please help?

Question

establish each identity:

a) cos ((3pi/2) + theta) = sin theta

b) cos (alpha + beta) + cos (alpha - beta) = 2cos alpha cos beta


please help me and explain, my book is horrible!!

Answer 1

Question a)
cos (3Π / 2) cos θ - sin (3Π / 2) sin θ
0 - (-1) sin θ
sin θ

Question b)
cos (α + β) = cos α cos β - sin α sin β
cos (α - β) = cos α cos β + sin α sin β
SUM = 2 cos α cos β

Answer 2

Answer the first question graphically, by tracing θ around couterclockwise
3/2π, whidh is 3/4 the way abound a circle. the y axis is pointing straight down. Then turn another θ degrees At this point The circle projects on the positive x axis. If you rotate
another π/2 degrees. the point on the circle will project on
the positive y axis the same as sin θ.

Ptolemy's Theorem is often used to derive the sum and
difference formulas. Check out this link:
http://books.google.com/books?id=ZCYtwHFVZHgC&pg=PA136&lpg=PA136&dq=trigonometry+product+identity&source=web&ots=oQFw_ylEP_&sig=-am0kG--EISUZmeaqqflzwMMKiw#PPA136,M1









αβγδεζηθικλμνξοπρςστυφχψω

Answer 3

use the formula cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

cos( (3pi/2) + theta) = cos(3pi/2)cos(theta) - sin(3pi/2)sin(theta)

since cos(3pi/2) = 0 and sin(3pi/2) = -1

so the answer is for (a) is sin(theta)

b) cos(a+b) + cos(a-b)
= cos(a)cos(b) - sin(a)sin(b) + cos(a)cos(b) + sin(a)sin(b)
= 2cos(a)cos(b)