Question

Prove the following
cos(π/2-x)cos(π/2-y)-sin(π/2-x)sin(π/2-y)=-cos(x+y)​

Answer 1

Answer:

Solution :

cosy⋅cos(π2-x)-cos(π2-y)cosx+sinycos(π2-x)+cosxsin(π2-y)=0

cosy⋅sinx-sinycosx+sinysinx+cosxcosy=0

sin(x-y)+cos(x-y)=0

sin(x-y)=-cos(x-y)

sin2(x-y)=cos2(x-y)

1-cos2(x-y)=cos2(x-y)

2cos2(x-y)=1

cos2(x-y)=12

cos(x-y)=±1√2

x-y=2nπ±π4

x=2nπ±π4+y.

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