Recall the double angle identity,
sin(2x) = 2 sin(x) cos(x)
Then we can write
sin(9x) cos(9x) = 1/2 sin(2 • 9x) = 1/2 sin(18x)
Then
∫ sin(9x) cos(9x) dx
= 1/2 ∫ sin(18x) dx
= -1/2 • 1/18 cos(18x) + C
= -1/36 cos(18x) + C
though you could continue with another double angle identity,
cos(2x) = cos²(x) - sin²(x)
to rewrite the antiderivative as
= -1/36 (cos²(9x) - sin²(9x)) + C
= 1/36 (sin²(9x) - cos²(9x)) + C
Let me edit your question to simplify it.
Eureka Math :
A)5 ÷ 1/3= ____.
B) There are ___ thirds in 1 whole.
C) There are ___ thirds in 5 wholes.
D) If 5 of 1/3, what is the whole? ___
E) 3 ÷1/5= ____ .
F) There are ___ fifths in 1 whole.
G) There are ___ fifths in 3 wholes.
H) If 3 of 1/5, what is the whole?___
Answer:
A) 15
B) three thirds
C) 15 wholes
D) whole is 2
E) 15
F) five fifths
G) 15 fifths
H) whole is 1
Step-by-step explanation:
A)
÷
÷
<u>Third:</u>
- third means
<u> </u>
B)
- To make 1 whole from thirds, we need three thirds i.e.

C)
- In 1 whole there are three thirds, so in 5 wholes there are
wholes.
D)
- In

- The whole of
or
is 2 (rounding 1.6 to 2)
E)
÷
<u>Fifth:</u> means 
F)
- To make 1 whole of fifths we need five fifths i.e.

G)
- In 1 whole we have 5 fifths, so in 3 wholes we have
fifths
H)
Answer:
0.255
Step-by-step explanation:
Answer:
for question two: 12
for question four: 1/3
for question six: 25.75 (rounded to two decimal places)
Answer:
(4,-3)
Step-by-step explanation:
is 4<3? no
is -2<3? yes but is 1>_ 8? no
etc etc