Question

Cos (x-y)/cos (x+y) = cotxcoty+1/cotxcoty-1

Answer 1

Answer:

Cos (x-y)/cos (x+y) = (cotxcoty+1)/(cotxcoty-1)

Step-by-step explanation:

Cos (x-y)/cos (x+y) = (cotxcoty+1)/(cotxcoty-1)

LHS = Cos (x-y)/cos (x+y)

Using Cos(A- B) = CosACosB + SinASinB

& Cos(A + B) = CosACosB - SinASinb

= (CosxCosy + SinxSiny)/(CosxCosy - SinxSiny)

Dividing numerator& Denominator by SinxSiny

= (CosxCosy/SinxSiny + 1)/((CosxCosy/SinxSiny - 1)

= ((cosx/Sinx).(cosy/(siny) + 1)/((cosx/Sinx).(cosy/(siny) - 1)

now CosA/SinA = CotA

= (CotxCoty + 1)/(CotxCoty - 1)

= RHS

QED

Proved

Cos (x-y)/cos (x+y) = (cotxcoty+1)/(cotxcoty-1)

Answer 2

Answer:

Step-by-step explanation:

Cos (x-y)/cos (x+y) = (cotxcoty+1)/(cotxcoty-1)

LHS = Cos (x-y)/cos (x+y)

Using Cos(A- B) = CosACosB + SinASinB

& Cos(A + B) = CosACosB - SinASinb

= (CosxCosy + SinxSiny)/(CosxCosy - SinxSiny)

Dividing numerator& Denominator by SinxSiny

= (CosxCosy/SinxSiny + 1)/((CosxCosy/SinxSiny - 1)

= ((cosx/Sinx).(cosy/(siny) + 1)/((cosx/Sinx).(cosy/(siny) - 1)

now CosA/SinA = CotA

= (CotxCoty + 1)/(CotxCoty - 1)

= RHS

QED

Proved

Cos (x-y)/cos (x+y) = (cotxcoty+1)/(cotxcoty-1)