Question

If (tanA+sinA)=m and (tanA-sinA)=n Prove that (m^2-n^2)=16mn

Answer 1

CRM

✌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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