Question

Hey guys !!

Plzz solve this problem ..

If Tan ø + sin ø = m, tan theta - sin theta = n, show that m² - n² = 4√mn.

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Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\boxed{\red{ SOLUTION:}}$

Substituting the value of m and n in L.H.S. and R.H.S.

L.H.S. = m² - n²

= (tan ∅ + sin∅ )² - (tan ∅ - sin ∅)²

= tan²∅ + sin²∅ + 2tan∅ sin∅ - (tan²∅ + sin²∅ - 2tan∅ sin∅)

= tan²∅ + sin²∅ + 2 tan∅ sin∅ - tan²∅ - sin²∅ + 2tan ∅ sin∅

= 4tan ∅ sin ∅

R.H.S. = 4√mn

= 4√(tan∅ + sin∅ ) (tan∅ - sin∅

= 4√tan²∅ - sin²∅

$= 4 \sqrt{ \frac{ {sin}^{2} \theta}{ {cos}^{2} \theta } - {sin}^{2} \theta}$

$= 4 \sqrt{ \frac{ {sin}^{2} \theta - {sin}^{2} \theta {cos}^{2} \theta }{ { cos}^{2} \theta} }$

$= 4 \sqrt{ \frac{ {sin}^{2} \theta(1 - {cos}^{2} \theta)}{ {cos}^{2} \theta} } = 4 \sqrt{ \frac{ {sin}^{2} \theta {sin}^{2} \theta}{ {cos}^{2} \theta} }$

= 4√tan²∅ sin²∅ = 4tan∅ sin∅

LHS = RHS

Hence proved.

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