Question

If cot theta =5/12 find the value of 5sin theta- 3cos theta /5 sin theta + 3cos theta

Answer 1

Answer:

If cot theta =5/12, the value of 5sin theta- 3cos theta /5 sin theta + 3cos theta 3/5

Step-by-step explanation:

Cot theta = Cosine theta / Sin theta

Cosine theta = adjacent / hypotenuse

Sin theta = Opposite / hypotenuse

Substituting in the first formula we have:

Cot theta = (adjacent / hypotenuse) / (Opposite / hypotenuse)

Cot theta = adjacent / opposite

Now, from the question, Cot theta = 5/12

Meaning, the adjacent side = 5 , and the opposite side = 12

Let's get the hypotenuse using Pythagorean theorem.

hypotenuse = √(12² + 5²) = 13

Cosine = 5/13

Sin = 12/13

Substituting this in the question we have:

[5(12/13) - 3(5/13) ] / [5(12/13) + 3(5/13)]

(60/13 - 15/13) / (60/13 + 15/13)

(45/13) / (75/13)

45/13 × 13/75

45/75 = 3/5

= 3/5

Answer 2

Answer:

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