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If cot A=(b)/(a),then prove that : ...

If `cot A=(b)/(a)`,then prove that :
`(asin - b cosA)/(sin A+bcosA)=(a^(2)-b^(2))/(a^(2)+b^(2))`

Text Solution

Verified by Experts

We have ,
L.H.S. `=(a sinA-bcosA)/(a sinA+bcosA)= (a(sinA)/(sinA)-b(cosA)/(sinA))/(a(sinA)/(sinA)+b(cosA)/(sinA))` (dividing Nr . And Dr . By sin A)
`(a-bcotA)/(a+bcotA)=(a-bxx(b)/(a))/(a+bxx(b)/(a))` (`:' cot A=(b)/(a))`
`((a^(2)-b^(2))/(a))/((a^(2)+b^(2))/(a))=(a^(2)-b^(2))/(a^(2)+b^(2))=`R.H.S
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