Question

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

Answer 1

Answer:

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

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}

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Answer 2

Given:

$5 \tan\theta = 4$

To Find:

$\frac{5sin \theta - 3cos \theta}{5sin \theta + 2cos \theta}$

Solution:

$5tan \theta = 4$

$= > tan \theta = \frac{4}{5}$

Now,

on dividing the Expression (under the heading 'to find') by cos theta in numerator and denominator, we get

$= \frac{5tan \theta - 3}{5tan \theta + 3}$

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

$= \frac{4 - 3}{4 + 3}$

$= \frac{1}{7}$