Question

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

Answer 1

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.

Answer 2

Please find in the attachment...

Hope it helps!!!