Question

cos(π/4+A)+cos(π/4-A) = √2 cos A

Answer 1

aap ke sawal ka jajab esi madhayam she

Answer 2

Hiii...............

Here Is Your Answer......

As we know,

cos(A+B)=cosA cosB - sinA sinB

cos(pi/4+A)= (cos pi/4)(cosA)-(sin pi/4)(sinA)

                   =(1/root 2) cosA -(1/root2)sinA....................(1.)

SIMILARLY,

cos(pi/4 -A)= (1/root2)cosA +(1/root2)sinA....................(2.)

AFTER ADDING EQUATION 1 AND 2

sinA(1/root2) will cancel so

we get,

cos (pi/4 +A)+cos(pi/4 -A)=2cosA(1/root2)..............(4.)

we know ,  (2/root2)=root2

put this in equation (4.)

hence on R.H.S it is

=(root2)cosA

SO,

L.H.S=R.H.S

HENCE PROVED................

HOPE IT HELPS YOU...

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THANKS FOR THIS OPPORTUNITY TO HELP YOU..  :) :)