Question

Given ; tanA + sin A=m and tanA - sin A=n Prove That (m square - n square) whole square=16mn

Answer 1

Solution:

Given ; tan A + sin A=m and tan A - sin A=n

To prove: (m² - n²) ²=16mn

Proof: LHS = (m²-n²)²
As we know the identity that, a²-b²=(a+b)(a-b)
=((m+n)(m-n))²
=((tan A +sin A +tan A - sin A)(tan A + sin A-(tan A - sin A)))²
=((2tan A)(tan A +sin A - tan A + sin A))²
=((2tan A)(2sinA))²
=(4tanAsinA)²
=16tan²Asin²A =16mn hence,proved

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