Question

If tan A+ sin A = m and tan A - sin A = n, then prove that m^2- n^2 = 4√mn​

Answer 1

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Given

tanA + sinA = m

and, tanA - sinA = n

To Prove

m² - n² = 4√mn

PROOF

LHS:

m² - n²

= (tanA + sinA)² - (tanA - sinA)²

= (tan²A + sin²A + 2tanAsinA) - (tan²A + sin²A - 2tanAsinA)

= 4tanAsinA

RHS:

4√mn = 4√(tanA + sinA)(tanA - sinA)

= 4√(tan²A)(sin²A)

= 4tanAsinA

Implies,LHS = RHS

Henceforth,proved

Answer 2

Heya!

Refer the attachment