Question

If 5 tan theta = 4, find the value of 2sin theta - 3cos theta/4sin theta - 9cos theta


ASAP!!

Thank you ❣️❣️​
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Answer 1

$\huge\mathfrak\green{Answer:-}$

It is given that 5 tan theta=4

So, tan theta=4/5

(2sin theta- 3cos theta)/(4sin theta-9cos theta)

Dividing both by cos theta, we get

(2sin theta- 3cos theta/cos theta)/(4sin theta-9cos theta/cos theta)

(2sin theta/cos theta -3cos theta/cos theta)/ (4sin theta/ cos theta -9cos theta / cos theta)

(2tan theta -3 )/(4tan theta - 9)

(2×4/5-3)/ (4×4/5-9)

(8/5×15/5)/(16/5-45/5)

(-7/5)/(-29/5)

=> 7/29

Answer 2

Given

→ 5 tan∅ = 4

→ tan∅ = 4/5

Solution

→ (2 sin∅ - 3 cos∅)/(4 sin∅ - 9 cos∅)

Dividing whole equation by cos∅. [Why? Because sin∅/cos∅ = tan∅]

→ (2 sin∅ - 3 cos∅)/cos∅/(4 sin∅ - 9 cos∅)/cos∅

→ (2 sin∅ - 3 cos∅)/cos∅/(4 sin∅ - 9 cos∅)/cos∅

→ (2 sin∅/cos∅ - 3 cos∅/cos∅)/(4 sin∅/cos∅ - 9 cos∅/cos∅)

→ (2 tan∅ - 3)/(4 tan∅ - 9)

→ (2 × 4/5 - 3)/(4 × 4/5 - 9)

→ (8/5 - 15/5)/(16/5 - 45/5)

→ (- 7/5)/(- 29/5)

→ 7/29

Hence the answer is 7/29.