Question

If \( 5 \tan \theta=4 \), then \( 6\left(\frac{5 \sin \theta-3 \cos \theta}{5 \sin \theta+2 \cos \theta}\right) \) is equal to

Answer 1

nandini4565, hello

When you simplify the expression, 

6 ( 5 sin θ − 3 cos θ) / ( 5 sin θ + 2 cos θ ) is equal to: 1

Answer 2

\(\tan(\theta) = \frac{4}{5}\)

\(\sin(\theta) = \frac{4}{\sqrt{41}}\)

similarly, 

\(\cos(\theta) = \frac{5}{\sqrt{41}}\)

put value and get your ans

Answer 3

Given that

Dividing the numerator and denominator by cos\(\theta\)

\(=6\frac{(5\,tan\theta-3)}{(5\,tan\theta+2)}\)

\(=6\frac{[5(\frac{4}{5})-3]}{[5(\frac{4}{5})+2]}\)

\(=6\frac{(4-3)}{(4+2)}\)

\(=6\times\frac{1}{6}\)

= 1