Question

if tan theta = under root minus 1 then find the value of tan theta divided by 1 plus tan square theta

Answer 1

$Hey\:There$(^-^)

Given, $\tan(a)= \sqrt{2} - 1$

$\frac{ \tan(a) }{1 + { \tan(a) }^{2} } = L.H.S.$

$= \frac{ \sqrt{2} - 1}{1 + {( \sqrt{2} - 1) }^{2} }$

$= \frac{ \sqrt{2} - 1 }{4 - 2 \sqrt{2} }$

$= \frac{ \sqrt{2} - 1}{4 - 2 \sqrt{2} } \times \frac{4 + 2 \sqrt{2} }{4 + 2 \sqrt{2} }$

$= \frac{( \sqrt{2} - 1)(4 + 2 \sqrt{2} ) }{ {(4})^{2} - ({2 \sqrt{2} })^{2} }$

$= \frac{4 \sqrt{2} + 4 - 4 - 2 \sqrt{2} }{16 - 8}$

$= \frac{2 \sqrt{2} }{8}$

$= \frac{ \sqrt{2} }{4}$

$= R.H.S.$

Answer 2

Hello friend

Good evening

Your answer is given in the attachment

i hope it will help you a lot

Thanks

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