Question

Find the maximum and minimum value of cos alpha ×cos beta ,whereas alpha +beta=45 degree

Answer 1

Answer:

max value:(2+√(2))/4

min value:√(2)/2

Step-by-step explanation:

cos(a)×cos(b)

=1/2(cos(a-b)+cos(a+b))    *identity*

=1/2(cos(a-b)+√(2)/2)      *a+b=45° and cos45°=√(2)/2*

=cos(a-b)/2+√(2)/4

cos(a-b) max value=1 for a-b=0:a=b=22.5°

              min value=√(2)/2

AS A RESULT,

max value=1/2+√(2)/4=(2+√(2))/4

min value=(√(2)/2)/2+√(2)/4=√(2)/2