Question

Example 9. If A + B = 45°, prove that (cot A-1) (cot B-1) = 2.Sol. A + B = 45°​

Answer 1

Cot (A+B) = (CotACotB-1)/(CotA + CotB )

We know......Cot(45)=1

so,          1=(CotACotB-1)/(CotA + CotB )

           CotACotB-1)=  (CotA + CotB )

           CotACotB-cotA-cotB=1

adding 1 to both sides.....we get

  

(cotA-1)(cotB-1)=2......proved

Hence proved....

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