Prove that
cos (a+b) + sin (a-b) = 2sin(45+a).cos(45+b)

Step-by-step explanation:

cos (A+B) + sin (A-B) = 2 sin (45°+A) cos (45° + B)

= 2 (sin45°cosA + cos45°sinA)(cos45°cosB - sin45°sinB)

But sin45=cos45 =(sqrt2)/2

= 2 ((sqrt2)/2 *cosA + (sqrt2)/2 *sinA)((sqrt2)/2 *cosB -(sqrt2)/2 *sinB)

= 2 ((sqrt2)/2 *(cosA + sinA))*((sqrt2)/2 *(cosB - sinB))

= 2*(sqrt2)/2 * (sqrt2)/2 * (cosA + sinA)*(cosB - sinB)

= (cosA + sinA)*(cosB - sinB)

= cosAcosB +sinAcosB -cosAsinB - sinAsinB

Regrouping:

= (cosAcosB- sinAsinB) + (sinAcosB -cosAsinB)

= cos (A+B) + sin (A-B)

median is the value separating the higher half of a data sample, a population or probablity distribution from the lower half.

step-by-step explanation:

say you have 3,8,7,3,1,9,8 order them from lowest to highest

if orderd it would be 1,3,3,7,8,8,9 now you take away from the lowest and the highest until you end up in the middle.

so you would remove the 1 and 9 leaving you with 5 digits remaining

when you've reached the middle that would be your answer so in this case the answer is 7

if there were two numbers left say 7 and 5 you'd and them together so 12 then divide by 2 witch would equal 6 so the answer would be 6

good luck on that project hoped i you at all

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)