Question

if 3 sec theta is equal to 5 then find the value of 5 sin theta minus 4 cos theta divided by 5 sin theta + 4 cos theta

Answer 1

Given that

$3 \sec( \alpha ) = 5$
So

$\\ \sec( \alpha ) = \frac{hypotenuse}{adjacent \: side} = \frac{5}{3}$
Therefore opposite side = √(5² - 3² ) = √ 16 = 4

To find :

$\frac{5 \sin( \alpha ) - 4 \cos( \alpha ) }{5 \sin( \alpha ) + 4 \cos( \alpha ) } \\ \\ = \frac{5 \times \frac{4}{5} - 4 \times \frac{3}{5} }{5 \times \frac{4}{5} + 4 \times \frac{4}{5} } \\ \\ = \frac{4 - \frac{12}{5} }{4 + \frac{12}{5} } \\ \\ = \frac{ \frac{20 - 12}{5} }{ \frac{20 + 12}{5} } \\ \\ = \frac{8}{32} \\ \\ = \frac{1}{4}$

Answer 2

3 sec theta =5, to find :- 5sin theta - 4cos theta /5sin theta + 4 cos theta.... Here is the answer✌️✌️✌️