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If tantheta +sintheta = m and tanthet...

If `tantheta +sintheta = m ` and `tantheta-sintheta=n`, then prove that `m^(2)-n^(2)=4sinthetatantheta`.

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Given that, ` tantheta +sintheta=m" "...(i)`
and `" "tantheta-sintheta=n" "...(ii)`
Now, `m+n = tantheta+sintheta + tantheta-sintheta` ltBrgt `m+n =2tan theta " "...(iii)`
Also, ` m-n =tantheta+sintheta- tan theta+sintheta` ltBrgt `m-n=2sintheta" "...(iv)`
From Eqs. (iii) and (iv),
`(m+n)(m-n)=4sintheta*tantheta`
`m^(2)-n^(2 )=4sintheta*tantheta` `" "` Hence proved.
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