Question

if 7 sinQ= 24 cosQ find the value of 2 sinQ+cosQ/3 sin Q-4 cosQ​

Answer 1

Answer:

i think this is your answer please check

Answer 2

Step-by-step explanation:

$7 \sin(q) = 24 \cos(q) \\ = > \: \frac{ \sin(q) }{ \cos(q) } = \frac{24}{7} \\ = > \tan(q) = \frac{24}{7} \\ \ = > \tan(q) = \frac{p}{b} = \frac{24}{7}$

$let \: p \: be \: 24 x \: \: and \: b \: be \: 7x \\ by \: using \: pythagoras \: theorem \: \\ {h}^{2} = {p}^{2} + {b}^{2} \\ = {(24x)}^{2} + {(7x)}^{2} \\ = \: {625x}^{2} \\ = > h \: = \sqrt{625 {x}^{2} } \\ = 25x$

$therefore \: \\ \sin(q) = \frac{24x}{25x} = \frac{24}{25} \\ \cos(q) = \frac{7x}{25x} = \frac{7}{25}$

$2 sin \: q+cos \: q/3 sin \: q-4 cos \: q \\ = \frac{2 \times 24}{25} + \frac{ \frac{7}{25} }{ \frac{3 \times 24}{25} } - 4 \times \frac{7}{25} \\ = \frac{20}{25} + \frac{7}{72} \\ = \frac{1540 + 175}{1800} \\ = \frac{1715}{1800}$

=343/360