Question

If 3x=sec theta and 3/x=tan theta,then find 9(x 2 -1/x 2 )

Answer 1

Here is your answer

Answer 2

Answer:

$The\: value \:of \:9(x^{2}-\frac{1}{x^{2}})=1$

Step-by-step explanation:

$3x=sec\theta ---(1)$

$\frac{3}{x}=tan\theta--(2)$

$The\: value \:of \:9(x^{2}-\frac{1}{x^{2}})\\=9x^{2}-\frac{9}{x^{2}}\\=(3x)^{2}-\big(\frac{3}{x}\big)^{2}\\=(sec\theta)^{2}-(tan\theta)^{2}\\=sec^{2}\theta-tan^{2}\theta\\=1$

/* By Trigonometric identity:

$\boxed {sec^{2}\theta-tan^{2}\theta=1}$*/

Therefore,

$The\: value \:of \:9(x^{2}-\frac{1}{x^{2}})=1$

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