I'm only going to alter the left hand side. The right side will stay the same the entire time
I'll use the identity tan(x) = sin(x)/cos(x) and cot(x) = cos(x)/sin(x)
I'll also use sin(x+y) = sin(x)cos(y)+cos(x)sin(y) and cos(x+y) = cos(x)cos(y)-sin(x)sin(y)
So with that in mind, this is how the steps would look:
tan(x+pi/2) = -cot x
sin(x+pi/2)/cos(x+pi/2) = -cot x
(sin(x)cos(pi/2)+cos(x)sin(pi/2))/(cos(x)cos(pi/2)-sin(x)sin(pi/2)) = -cot x
(sin(x)*0+cos(x)*1)/(cos(x)*0-sin(x)*1) = -cot x
(0+cos(x))/(-sin(x)-0) = -cot x
(cos(x))/(-sin(x)) = -cot x
-cot x = -cot x
Identity is confirmed
3√10^4x is equivalent to -√10 3/4^x and -4√10^3x they are all equivalent
Three hundred and ten million, seven hundred and sixty three thousand, one hundred and thirty six.
I don't think you're stupid. ^^
Let's take the third term, 8. If n=3, then an should be 8.
The first answer gives 15+2.5*3=22.5.
The second answer gives 15.5+2.5=23.
The third answer gives 15-2.5*3=7.5.
The fourth answer gives 15.5-2.5*3=8.
Choice 4 is correct.
Let's try to actually find the equation on our own.
The equation for an arithmetic series is an=a0+dn where a0 is the term that comes before the first term.
The first term given is 13 and it decreases by 2.5 each time so n=-2.5 and the term that would be before 13 is 15.5.
Thus the equation is an=15.5-2.5n
