Question

Is sin theta + cos theta upon sin theta minus cos theta equals to 5 by 3 then find the value of 7 tan theta + 2 upon 2 tan theta + 7?

Answer 1

check the attachment

Answer 2

Answer:

The correct answer to this question is:

(7 tan θ + 2) / (2 tan θ + 7) = 2

Step-by-step explanation:

Given,

(sin θ + cos θ) / (sin θ - cos θ) = 5 / 3    (equation 1)

To find, (7 tan θ + 2) / (2 tan θ + 7) =?

from equation 1,

(sin θ + cos θ) / (sin θ - cos θ) = 5 / 3

( sin θ + cos θ ) * 3 = 5 * ( sin θ - cos θ )

3 sin θ + 3 cos θ = 5 sin θ - 5 cos θ

3 cos θ + 5 cos θ = 5 sin θ - 3 sin θ

8 cos θ = 2 sin θ

8 / 2 = sin θ / cos θ

4 = tan θ

∴ tan θ = 4

(7 tan θ + 2) / (2 tan θ + 7)

= ( 7 * (4) + 2 ) / ( 2 * (4) + 7 )

= (28 + 2) / (8 + 7)

= (30) / (15)

= 2

Hence, (7 tan θ + 2) / (2 tan θ + 7) = 2

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