If 7 sin theta = 24 cos theta find value of 2 sin theta + cos theta ________________ 3 sin theta – 4

Question

If 7 sin theta = 24 cos theta find value of
2 sin theta + cos theta
________________
3 sin theta – 4 cos theta

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Melody 2 weeks 2021-09-07T11:55:15+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-09-07T11:56:54+00:00

    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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