Answer:
Step-by-step explanation:
Given the expression cosec (x) = 4 and tan(x)< 0
since cosec x = 1/sinx
1/sinx = 4
sinx = 1/4
From SOH, CAH TOA
sinθ = opposite/hypotenuse
from sinx = 1/4
opposite = 1 and hypotenuse = 4
to get the adjacent, we will use the Pythagoras theorem
adj² = 4²-1²
adj² = 16-1
adj ²= 15
adj = √15
cosx = adj/hyp = √15/4
tanx = opposite/adjacent = 1/√15
since tan < 0, then tanx = -1/√15
From double angle formula;
sin2x = 2sinxcosx
sin2x = 2(1/4)(√15/4)
sin2x = 2√15/16
sin2x = √15/8
for cos2x;
cos2x = 1-2sin²x
cos2x = 1-2(1/4)²
cos2x = 1-2(1/16)
cos2x= 1-1/8
cos2x = 7/8
for tan2x;
tan2x = tanx + tanx/1-tan²x
tan2x = 2tanx/1-tan²x
tan2x = 2(-1/√15)/1-(-1/√15)²
tan2x = (-2/√15)/(1-1/15)
tan2x = (-2/√15)/(14/15)
tan2x = -2/√15 * 15/14
tan2x = -30/14√15
tan2x = -30/7√15
rationalize
tan2x = -30/7√15 * √15/√15
tan2x = -30√15/7*15
tan2x = -2√15/7
Answer:

Step-by-step explanation:
Evan spent 20 hours doing homework last week
25 hours were spent this week.
<u>Let's see what 125% of 20 equals:</u>
= (125 / 100) * 20
= (125 / 10) * 2
= 125 / 5
= 25 hours
But,
<u>It is written that Evan thought he spent 125 % more than the last week which means:</u>
= (125% of 20) + 20
= 25 + 20
= 45 hours
He should've said that he has given 25% more time than the last week.
(<u>Note that:</u> 25 % of 20 equals 5 so 25 % more than last week will be equal to (25 % + 20) = (5+20) = 25)
![\rule[225]{225}{2}](https://tex.z-dn.net/?f=%5Crule%5B225%5D%7B225%7D%7B2%7D)
Hope this helped!
<h3>~AH1807</h3>
Hi, yes ive been struggling with like terms.
Answer: There are 60 ways that they can travel to the concert.
Step-by-step explanation:
Since we have given that
Number of people want to go to a concert = 12
Number of cars = 3
Number of drivers in the group = 5
So, using the "Fundamental theorem of counting":
We get that

Hence, there are 60 ways that they can travel to the concert.