Tan x /(1 +sec x) + (1+sec x) /tan x
Tan x=sin x / cos x
1+ sec x=1 +1/cos x=(cos x+1)/cos x
Therefore:
tan x /(1 +sec x) =(sin x/cos x)/(cos x+1)/cos x=
=(sin x * cos x) / [cos x* (cos x+1)]=sin x /(Cos x+1)
(1+sec x) /tan x=[(cos x+1)/cos x] / (sin x/cos x)=
=[cos x(cos x+1)]/(sin x *cos x)=(cos x+1)/sin x
tan x /(1 +sec x) + (1+sec x) /tan x=
=sin x /(Cos x+1) + (cos x+1)/sin x=
=(sin²x+cos²x+2 cos x+1) / [sin x(cos x+1)]=
Remember: sin²x+cos²x=1⇒ sin²x=1-cos²x
=(1-cos²x+cos²x+2 cos x+1) / [sin x(cos x+1)]=
=2 cos x+2 / [sin x(cos x+1)]=
=2(cos x+1) / [sin x(cos x+1)]=
=2 /sin x
Answer : tan x /(1 +sec x) + (1+sec x) /tan x= 2/sin x
Answer:
The expression is 10t = 65
Step-by-step explanation:
At the point where the local train and the express train meet, both trains would have travelled an equal distance.
A local train leaves the station in Springfield traveling toward New York City at a constant rate of 55 mph.
Let t represent the time it spent in travelling a given distance.
Distance = speed × time
Therefore,
Distance travelled by the local train is 55 × t = 55t
The express train headed for New York City on the same route leaves the station 1 hour later. The rate of the express train is 65 mph. It means that total time spent travelling the same distance as the local train is t - 1
Therefore, distance travelled is
65(t - 1)
Since the distance travelled is the same, therefore,
55t = 65t - 65
65t - 55t = 65
10t = 65
<span>x is the total number of liters of orange juice and water combined. 80% of the mixture is pure orange juice which means 20% of it is water. Therefore, x 20/100 = 1 is the equation in single variable that can be used to find x. and 20/100 is 1/5 so there are 5 total liters in all and 5-1 is 4, so there are 4 liters of orange juice in the can. Hope this helps :)</span>
Answer:the height of the flagpole is 27.12 ft
Step-by-step explanation:
The wire makes an angle with the ground and forms a right angle triangle with the flag pole. The length of the wire represents the hypotenuse of the right angle triangle. The height of the flag pole and the ground distance from the wire represents the adjacent and opposite sides respectively.
To determine the height of the flagpole, x we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
31² = x² + 15²
x² = 961 - 225 = 736
x = √736. = 27.12 ft
