Question

if m=tanA-sinA ,n=tanA-sinA, prove that m²-n²=16mn​

Answer 1

Step-by-step explanation:

m=tanA+sinA, n=tanA-sinA

m²-n²=(tanA+sinA)²-(tanA-sinA)²

m²-n²={tan²A+2tanAsinA+sin²A} -{tan²A-2tanAsinA+sin²A}

m²-n²=tan²A+2tanAsinA+sin²A-tan²A. +2tanAsinA-sin²A

m²-n²=4tanAsinA

(m²-n²)²=16tan²Asin²A

(m²-n²)²=16{tan²A(1-cos²A)

=16{tan²A-tan²Acos²A}

=16(tan²A-sin²A)

=16(tanA-sinA)(tanA-sinA)(m²-n²)²=16mn