Question

if tanx+sinx= m and tanx- sinx= n show that m square- n square =4 underroot mn​

Answer 1

Answer:

given that

Tanx+sinx=m be equation no 1

Tanx-sinx=n be equation no 2

from equation no 1

Tanx=m-sinx

substitute in equation no 2

m-sinx-sinx=n

m-sinx=n+sinx

squaring on both sides

(m-sinx)2=(n+sinx)2

M2+sin2x-2msinx=n2+sin2x+2nsinx

m2-n2=2msinx+2nsinx

4mnsinx hence proved