Question

if sin thita = 4/5, calculate

5sin thita - 3cos thita ________________
2cos thita - 2sin thita​

Answer 1

Step-by-step explanation:

5 tan theta=4

So tan theta=4/5

therefore, sin theta/cos theta = 4/5

Hence we can say that,

sin theta= 4x , cos theta= 5x

So, (5 sin theta - 3 cos theta)/(5 sin theta+ 2 cos theta)

      = (20x-15x)/(20x+10x)

      = 5x/30x=1/6

Answer 2

Given :

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

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

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

→ $\frac{20 -15}{20+ 10}$

→ $\frac{5}{30}$

→ $\frac{1}{6}$