Question

If tan = 3, then what is the value of
[5sintheta-3costheta/4sintheta+3costheta]?​

Answer 1

Answer:

tan = 3

if ABC is a right angeled triangle and right angled at B

so tan = $\frac{opposite \: side}{Adjacent \: Side}$

tan = $\frac{3}{1}$

from the value of tan

AB = 3

BC = 1

AC = ?

$From \: pythagores \: Thereom$

${AC}^{2}={AB}^{2}+{BC}^{2}$

${AC}^{2}={3}^{2}+{1}^{2}$

${AC}^{2} = 9+1=10$

${AC}= \sqrt{10}$

From the above values

sin = AB/AC

sin =

$\frac{3}{ \sqrt{10} }$

cos = BC/AC

cos =

$\frac{1}{ \sqrt{10} }$

so

5 sin - 3 cos / 4 sin + 3 cos

$= \frac{5 \times \frac{3}{ \sqrt{10} } - 3 \times \frac{1}{ \sqrt{10} } }{4 \times \frac{3}{ \sqrt{10} } + 3 \times \frac{1}{ \sqrt{10} } } \\ = \frac{ \frac{15}{ \sqrt{10} } - \frac{3}{ \sqrt{10} } }{ \frac{12}{ \sqrt{10} } + \frac{3}{10} } \\ = \frac{ \frac{15 - 3}{ \sqrt{10} } }{ \frac{12 + 3}{ \sqrt{10} } } \\ = = > \frac{12}{15} = \frac{4}{5}$