Question

If 4 cot theta = 5 show that 5 sin theta + 3 cos theta / 5 sin theta - 2 cos theta =7/2

Answer 1

Step-by-step explanation:

Given that: If 4 cot theta = 5 show that 5 sin theta + 3 cos theta / 5 sin theta - 2 cos theta =7/2

Solution:

Expression

if

$4cot \theta = 5 \\ \\ cot \theta = \frac{5}{4}$

Then prove that

$\frac{5sin \theta + 3 cos\theta }{5sin \theta\: - 2 cos \theta} = \frac{7}{2}$

First of all take sin theta common from numerator and denominator ,

As we know that

$cot \theta = \frac{cos \theta}{sin \theta}$

$\frac{5sin \theta + 3 cos\theta }{5sin \theta\: - 2 cos \theta} = \frac{sin \theta \bigg(5 + 3\frac{cos \theta}{sin \theta} \bigg)}{sin \theta \bigg(5 - 2 \frac{cos \theta}{sin \theta} \bigg) } \\ \\ = \frac{5 + 3cot \theta}{5 - cot \theta } \\ \\ = \frac{5 + 3 (\frac{5}{4}) }{5 - 2 (\frac{5}{4} ) } \\ \\ = \frac{5 + \frac{15}{4} }{5 - \frac{10}{4} } \\ \\ = \frac{20 + 15}{4} \times \frac{4}{20 - 10} \\ \\ = \frac{35}{10} \\ \\ = \frac{7}{2} \\ \\ = RHS$

Hence proved

Hope it helps you.

Answer 2

Answer:

Here is your answer in the attachment