Question

given tantheta=4/3

evaluate please​

Answer 1

SOLUTION:-

Given:

$tan \theta = \frac{4}{3} = \frac{</u><u>P</u><u>}{</u><u>B</u><u>}$

Therefore,

Perpendicular= 4

Base= 3

We find Hypotenuse:

SO,

Using Pythagoras theorem:

${H}^{2} = {P}^{2} + {B}^{2} \\ \\ = > {H}^{2} = {4}^{2} + {3}^{2} \\ \\ = > {H}^{2} = 16 + 9 \\ \\ = > {H}^{2} = 25 \\ \\ = > H = \sqrt{25} \\ \\ = > H = 5$

Now,

$we \: know \: that \: sin \theta = \frac{P}{H} = \frac{4}{5}$

&

$we \: know \: that \: co s \: theta = \frac{B}{H} = \frac{3}{5}$

Evaluate:

$\frac{2sin \theta \times cos \theta}{cos {}^{2} \theta - {sin}^{2} \theta } \\ \\ = > \frac{2 \times \frac{P}{H} \times \frac{B}{H} }{( { \frac{B}{H} )}^{2} - ( { \frac{P}{H} )}^{2} } \\ \\ = > \frac{2 \times \frac{4}{5} \times \frac{3}{5} }{( { \frac{3}{5} )}^{2} - ( { \frac{4}{5} )}^{2} } \\ \\ = > \frac{ \frac{24}{25} }{ \frac{9}{25} - \frac{16}{25} } \\ \\ = > \frac{ \frac{24}{25} }{ - \frac{7}{25} } \\ \\ = > \frac{24}{25} \times \frac{25}{ - 7} \\ \\ = > - \frac{24}{7}$

Hope it helps☺️