Given data
<span>sin (x+pi/2)=cos x
</span>now using sin law
sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
now using above values
sin(pi/2+x)=sin(pi/2)cos(x)+cos(pi/2)sin(x)
as we know that
sin(pi/2)=1
cos(pi/2)=0
now putting these values
sin(pi/2+x)=1*cosx+0*1
sin(pi/2+x)=cosx
hence proved that
<span>sin (x+pi/2)=cos x</span>
The solution to the system of inequalities given is: 
<h3>What is the solutions to a system of inequalities?</h3>
The solution is the set of values that respect all conditions of the system.
The first condition is:
The second condition is:
The intersection of the conditions, which is the solution to the inequality, is:
More can be learned about a system of inequalities at brainly.com/question/3656398
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Answer:
500 minutes
Step-by-step explanation:
Ok, so the first thing we want to do is figure out how long it takes to complete one lap.
So if it takes 10 minutes to travel 2 laps lets find out how many minutes for one.
It would be 5 minutes for one lap, if you divide 10 by 2 because of the 2 laps.
Next, you just multiply the 5 minutes by 100 laps:
This gives you 500 minutes.
Hope this helps :)
