Question

If 5 tan theta = 4 find the value of 5 sin theta - 3 cos theta/5 sin theta + 2 cos theta

Answer 1

Answer:

$\frac{1}{6}$

Step-by-step explanation:

Given that ,

5 tan theta = 4

tan theta = 4/5

We know that

tan theta = Sin theta/Cot theta

 Say X

Sin theta = 4x

Cos theta = 5x

Evaluate the values of LHS Side

$\frac{5 \ Sin\theta - 3\ Cos\theta}{5\ Sin\theta +  \ 2Cos\theta}$

=> $\frac{(5 * 4 )- (3 * 5) }{(5 * 4) + (2 * 5)}$

=> $\frac{20 -15}{20+ 10}$

=> $\frac{5}{30}$

=> $\frac{1}{6}$

Hence Proved

Answer 2

Answer:

1/6 is the answer of the expression  5 sin theta - 3 cos theta/5 sin theta + 2 cos theta.

Step-by-step explanation:

Given,

5 tan θ = 4

tan θ = 4/5

Now,

(5 sin θ – 3 cos θ)/(5 sin θ + 2 cos θ)

Dividing the numerator and denominator by cos θ,

= (5 tan θ – 3)/(5 tan θ + 2)

= [5(4/5) – 3]/ [5(4/5) + 2]

= (4 – 3)/(4 + 2)

= 1/6

#spj2