Answer:
see explanation
Step-by-step explanation:
(4)
consider the left side
factor the numerator
cosx - cos³x = cosx(1 - cos²x)
![\frac{cosx(1-cos^2x)}{sinx}[/tex = [tex]\frac{cosxsin^2x}{sinx}](https://tex.z-dn.net/?f=%5Cfrac%7Bcosx%281-cos%5E2x%29%7D%7Bsinx%7D%5B%2Ftex%20%3D%20%5Btex%5D%5Cfrac%7Bcosxsin%5E2x%7D%7Bsinx%7D)
cancel sinx on numerator/denominator
= cosxsinx =right side ⇒ verified
(5)
Consider the left side
expand the factors
(1 + cotΘ)² + (1 - cotΘ)²
= 1 + 2cotΘ + cot²Θ + 1 - 2cotΘ + cot²Θ
= 2 + 2cot²Θ
= 2(1 + cot²Θ) ← 1 + cot²Θ = cosec²Θ
= 2cosec²Θ = right side ⇒ verified
(6)
Consider the left side
the denominator simplifies to
cosxtanx = cosx × 
= sinx
= sinx( 
+ 
)
= + 
= tanx + 1 = right side ⇒ verified
Answer:
[three sixths] are the same amount as [one half]
Step-by-step explanation:
Call these units thirds. Split these units in half so there are twice as many. Call these units sixths because six of them make one.
Answer:
d) 2x(4x + 2)
Step-by-step explanation:
a) 4(2x + 1) = 8x + 4
b) 1/2(16x + 8) = 8x + 4
c) 2(4x + 2) = 8x + 4
d) 2x(4x + 2) = 8x² + 4x
1). The inequality says "height is 54 or more".
Any height that is less than 54 does NOT qualify.
2). The sign says "Maximum total weight 800 pounds".
Any weight that's 800 pounds or less is OK.
3). Paula has scored 21, 25, and 15 points.
. . . . . they're NOT all greater than 21
. . . . . they ARE all 25 or less
. . . . . they ARE all less than 30
. . . . . they ARE all 10 or more .
4). First, write down the number of cans that
each student collected, but arrange them in order.
Then check each choice.
A). misses the highest 3 students completely
B). includes everybody
C). misses the lowest 3 students completely
D). OK, but the first and last intervals aren't needed,
because nobody's cans are in those intervals
