If acos(x+α)=bcos(x-α) show that (a+b)tanx=(a-b)cotα

Steps to prove If acos(x+α)=bcos(x-α) show that (a+b)tanx=(a-b)cotα

From Question given that

⇒acos(x+α)=bcos(x-α)

By componendo and dividendo

⇒(a+b)/(a-b)={cos(x-α)+cos(x+α)}/{cos(x+α)+cos(x-α)}

⇒(a+b)/(a-b)=2.cosx.cosα/2.sinx.cosα

⇒(a+b)/(a-b)=cotx.cotα

⇒(1/cotx)(a+b)=(a-b)cotα

⇒(a+b)tanx=(a-b)cotα

Hence (a+b)tanx=(a-b)cotα is proved.

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