Question

please answer my question ​

Answer 1

Answer:

$given \: = \sec(x) + \tan(x) = a \\ then \: {a}^{2} = {( \sec \: x + \tan \: x) }^{2} \\ {a}^{2} = { \sec }^{2} x + { \tan}^{2} x + 2 \sec \: x \: \tan \: x......(1) \\ {a}^{2} = 2 { \sec }^{2} x - 1 + 2 \sec \: x \: \tan \: x \\ {a}^{2} + 1 = 2 \sec \: x( \sec \: x + \tan \: x) .......(2) \\ Consider \: equation \: (1) \\ {a}^{2} = 2 { \tan }^{2} x \: + 1 + 2 \sec \: x \tan \: x \\ {a}^{2} = 2 \tan \: x( \sec \: x \: + tan \: x)......(3) \\ Divide \: (2) \: and \: (3) \\ \frac{ {a }^{2} - 1 }{ {a}^{2} + 1 } = \frac{2tan \: x( \sec \: x + tan \: x) }{2sec \: x(sec \: x + tan \: x)} = sin \: x</p><p></p><p>$

Answer 2

Step-by-step explanation:

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