Question

If 7 sin 0 = 24 cos ,
2 sin +cos O
Find the value of
3 sin 0-4 cos O​

Answer 1

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Step-by-step explanation:

$\large\bf{\underline{\red{Given✔}}}$

7 sin θ = 24 cos θ .

$\large\bf{\underline{\red{To -Find✔}}}$

(2 sin θ + cos θ) / (3 sin θ - 4 cos θ) = ?

$\large\bf{\underline{\red{Solution✔}}}$

→ 7 sin θ = 24 cos θ .

→ sin θ / cos θ = 24/7

→ tan θ = 24/7

now,

→ (2 sin θ + cos θ) / (3 sin θ - 4 cos θ)

dividing numerator and denominator by cos θ we get,

→ [(2sin θ/cos θ) + (cos θ/cos θ) / [(3sin θ/cos θ) - (4cos θ/cos θ)]

→ [2 tan θ + 1] / [3 tan θ - 4]

Putting value of tan θ now,

→ [(2*24/7) + 1] / [(3*24/7) - 4]

→ [(48/7) - 1] / [(72/7) - 4]

→ [(48 - 7)/7] / [(72 - 28)/7]

→ (41/7) / (44/7)

→ (41/7) * (7/44)

→ (41/44) (Ans.)

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Answer 2

Step-by-step explanation:

(2 sin 0 + cos 0) / (3 sin 0-4 cos 0)

dividing numerator and denominator by cos e we get,

[(2sin 0/cos 8) + (cos 0/cos 0) / [(3sin 8/cos 8) - (4cos e/cos 8)]

- [2 tan 0 + 1] / [3 tan 0 - 4]

Putting value of tan 8 now,

→ [(2*24/7) + 1] / [(3*24/7) - 4]

[(48/7) - 1] / [(72/7) - 4]

[(48-7)/7] / [(72-28)/7] (41/7) / (44/7)

→ (41/7) * (7/44) -

-> (41/44) (Ans.)