Answer:
See proof below
Step-by-step explanation:
show that
sinx/1+cosx=tanx/2
From LHS
sinx/1+cosx
According to half angle
sinx = 2sinx/2 cosx/2
cosx = cos²x/2 - sin²x/2
cosx = cos²x/2 - (1- cos²x/2)
cosx = 2cos²x/2 - 1
cos x + 1 = 2cos²x/2
Substitute into the expression;
sinx/1+cosx
= (2sinx/2 cosx/2)/2cos²x/2
= sinx.2/cos x/2
Since tan x = sinx/cosx
Hence sinx/2/cos x/2 = tan x/2 (RHS)
This shows that sinx/1+cosx=tanx/2
The event "Atleast once" is the complement of event "None".
So, the probability that Marvin teleports atleast once per day will the compliment of probability that he does not teleports during the day. Therefore, first we need to find the probability that Marvin does not teleports during the day.
At Morning, the probability that Marvin does not teleport = 2/3
Likewise, the probability tha Marvin does not teleport during evening is also 2/3.
Since the two events are independent i.e. his choice during morning is not affecting his choice during the evening, the probability that he does not teleports during the day will be the product of both individual probabilities.
So, the probability that Marvin does not teleport during the day = 
Probability that Marvin teleports atleast once during the day = 1 - Probability that Marvin does not teleport during the day.
Probability that Marvin teleports atleast once during the day = 
First, we have to find the length of each side of triangle. Equilateral triangle means 3 sides r in same length, so each side will be 21 ÷ 3 = 7
Now we need to calculate the height of the triangle. We can do this by Pythagoras theorem
Let the height be h
(7/2)^2 + x^2 = 7^2
The area should be 6.0621778265
Or u can say 6.06 corrected to 3 sig fig