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Prove that ((a+b+c)(b+c-a)(c+a-b)(a+b-c)...

Prove that `((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2c^2)=sin^2A`

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`((a + b + c) (b + c -a) (c + a - b) (a + b -c))/(4b^(2) c^(2))`
`= (2s 2 (s - a) 2 (s -b) 2 (s -c))/(4b^(2) c^(2))`
`= (4 Delta ^(2))/(b^(2) c^(2))`
`= (4)/(b^(2) c^(2)) ((1)/(2) bc sin A)^(2) = sin^(2) A`
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CENGAGE ENGLISH-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. Find the value of tan A, if area of Delta ABC is a^(2) -(b-c)^(2).

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  2. Prove that a^(2) sin 2B + b^(2) sin 2A = 4 Delta

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  3. Prove that ((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2c^2)=sin^2A

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