Write the product as a sum or difference.
18cos(29x)cos(17x)
select the correct answer below:

9sin(46x)+9sin(12x)

9sin(46x)−9sin(12x)

9cos(46x)+9cos(12x)

9cos(46x)−9cos(12x)

9cos(46x)+9sin(12x)

9sin(46x)−9cos(12x)

9cos(46x) + 9cos(12x)

Step-by-step explanation:

18cos(29x)cos(17x)

According to Product-Sum identities

cos(α)cos(β)= (1/2)[cos(α+β)+cos(α-β)]

Putting α=29x and  β=17x in Product-Sum identity we get

= 18×(1/2)[cos(29x+17x)+cos(29x-1`7x)]

Dividing 18 by 2 we get 9

= 9[cos(46x)+cos(12x)]

Multiplying 9 with both the terms we get

= 9cos(46x)+9cos(12x)

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional