Question

if 7 sin theta= 24 cos theta. find the value of 2 sin theta+ cos theta / 3 sin theta -4 cos theta ​

Answer 1

Given :-

• 7 sin θ = 24 cos θ .

To Find :-

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

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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