if sec A + tan A = p, prove that sin A=p2-1/p2+1

sec A + tan A = p

(1 + sinA)/cosA = p

(1 + sinA) = pcosA

Square on both sides, 

1 + 2sinA + sin²A = p²cos²A

1 + 2sinA + sin²A = p²(1 - sin²A)

1 - p² + 2sinA + (1 + p²)sin²A = 0

This is a quadratic equation in sinA, the roots are,

sinA = {-2 ± [4 - 4(1 - p²)(1 + p²)]^1/2}/ 2(1 + p²)

sinA = {-2 ± [4 - 4(1 - p⁴)]^1/2}/ 2(1 + p²)

sinA = {-2 ± [4p⁴]^1/2}/ 2(1 + p²)

sinA = {-2 ± 2p²}/ 2(1 + p²)

 sinA = {p² - 1}/(1 + p²)    .. taking the positive root.

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