Question

Cos ( a+b) + sin ( a-b) =2 sin (45+a) cos (45+b)

Answer 1

Answer:

GIVEN:--

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

LHS:--

Cos(A + B) + sin(A - B)

cosAcosB - sinAsinB + sinAcosB - cosAsinB

RHS

2(sin45°cosA+cos45°sinA)X

(cos45cos-sin45sinB)

2(√2/2cosA + √2/2sinA)X

(√2/2cosB - √2/2sinB)

2( (1/2)cosAcosB - (1/2)cosAsinB

+

(1/2)sinAcosB - (1/2)sinAsinB)

cosAcosB - cosAsinB + sinAcosB - sinAsinB

LHS = RHS

HOPE THIS HELPS

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

cos(a+b)=cosacosb-sinasinb

sin(a-b)=sinacosb-cosasinb

sin45+a=sin45cosa+cos45sina=(cosa+sina)/sqrt(2)

cos45+b=cos45cosb-sin45sinb=(cosb-sinb)/sqrt(2)

RHS: 2sin(45+a)cos(45+b)=2(cosa+sina)(cosb-sinb)/2=(cosa+sina)(cosb-sinb)

LHS:

cosacosb-sinasinb+sinacosb-cosasinb

=cosb(sina+cosa)-sinb(sina+cosa)

=(sina+cosa)(cosb-sinb)

LHS=RHS