Whatre the steps in verifying the identity sin(x-y)/sin y + cos (x-y)/cos y = sinx/(sinycosy) ?

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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Let (x-y) =k

 

sin(x-y)/sin y + cos (x-y)/cos y

= sink/siny+cosk/cosy

=(sink*cosy+cosk*siny)/(siny.cosy)

 

we know that sin(A+B) = sinA*cosB+cosA*sinB

Therefore (sink*cosy+cosk*siny) = sin(k+y)

Since k=x-y

sin(k+y) = sin(x-y+y)=sinx

 

Therefore;

sin(x-y)/sin y + cos (x-y)/cos y

=(sink*cosy+cosk*siny)/(siny.cosy)

=sin(k+y)/(siny.cosy)

=sinx/(siny.cosy)

 

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