Question

if tan A + sinA = m , tan A - sinA=n .Then prove that (m^2-n^2)^2 = 16mn​

Answer 1

Answer:

Solution:-

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.  

proved.

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