If (tanA+sinA)=m and (tanA-sinA)=n Prove that (m^2-n^2)=16mn
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✌m = tanA + sinA
✌n = tanA - sinA
✌L.H.S. = {(tanA + sinA)² - (tanA-sinA)²}
{tan²A + sin²A + 2tanAsinA - (tan²A + sin²A -2tanAsinA)}²
✌✌(4tanAsinA)²
✌✌16tan²Asin²A
✌✌16tan²A(1 - cos²A)
✌✌16tan²A - tan²Acos²A
✌✌16tan²A - sin²A/cos²A × cos²A
✌✌16tan²A - sin²A
✌✌16(tan²A + sin²A) (tan²A - sin²A)
✌✌16 mn
R.H.S. = L.H.S.
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