Solution:
<u>We know that:</u>
<em>Since we are already given the base and the height, we can substitute them into the formula to find the area of the triangle.</em>
<u>Cancel out the "2" by dividing it by 18.</u>
<u>Simplify the multiplication.</u>
Answer:
cool
Step-by-step explanation:
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:
= 2
= k(k+1)
= (k+1)(k+2)
Step-by-step explanation:
We are given the statement,
as 2 + 4 + 6 + . . . + 2n = n(n+1)
That is,
as 2 + 4 + 6 + . . . + 2n = 
So, we have,
= 
= 2
= 
= 2 + 4 + 6 + . . . + 2k = k(k+1)
= = 2 + 4 + 6 + . . . + 2k + 2(k+1) = (k+1)(k+2)
Thus, we get,
= 2
= k(k+1)
= (k+1)(k+2)
