Question

if tanA + sinA = m and tanA - sinA= n prove that (m²-n²)=16​

Answer 1

anA +sinA = m,

TanA- sinA = n,

Now LHS,

m² - n²

(tanA + sinA)² - (tanA - sinA)²

(tan²A + sin² A + 2tanAsinA ) - ( tan²A + sin²A - 2tanAsinA)

tan²A + sin²A +2 tanA sinA -tan²A -sin²A +2tanA sinA

4tanA sinA ______ (1)

Now RHS,

16mn

16(tanA + sinA) ( tanA - sinA)

16( tan²A - sin² A) _______[a² - b² = ( a+ b ) (a- b)]

16 tan²A ( 1-cos²A)

16 tan²A sin²A

(4 tanA sinA)²

Here we can see LHS is not equal to RHS.