Question

Heya mates!!

❤️❤️❤️❤️❤️❤️

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


ASAP!!

Thank you ❣️❣️​

Answer 1

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.

Answer 2

Given :-

» 5 tanΦ = 4

» tanΦ = 4/5

SOLUTION :-

(2sinΦ - 3cosΦ)/(4sinΦ - 9cosΦ)

Devide all by cos Φ

(2sinΦ - 3cosΦ)/cosΦ/(4sinΦ - 9cosΦ)/ cosΦ

» (2tanΦ - 3)/(4tanΦ - 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