Question

if sec theta = 5/4 then evaluate tan theta/ 1+ tan^2 theta

Answer 1

I guess it's ryt. just check it out

Answer 2

Answer:

9/12

Explanation:

We have , $sec\theta = \frac{5}{4}$----(1)

Now,

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

$tan^{2}\theta = \left(\frac{5}{4}\right)^{2}-1$

$=\frac{5^{2}}{4^{2}}-1$

$=\frac{25}{16}-1$

$=\frac{(25-16)}{16}$

$=\frac{9}{16}$

$tan\theta = \frac{3}{4}$----(2)

Now ,

$\frac{tan^{2}\theta}{1+tan^{2}\theta}$

= $\frac{tan^{2}\theta}{sec^{2}\theta}$

= $\frac{\frac{9}{16}}{\frac{25}{16}}$

=$\frac{9}{25}$

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