Question

Heya mates!!

❤️❤️❤️❤️❤️❤️

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

Answer:

1/6

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

Answer:

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.