Question

if 3cot theta =2 find the value of 4 sin theta - 3cos theta / 2sin theta +6cos theta​

Answer 1

Answer:

cot Ф =2/3

so, adjacent= 2k opposite= 3k

where k is constant

Opp² + adj² = hypo²

4k² + 9k² = hypo²

13k² = hypo²

hypo= k√13

sin Ф= opp/hypo = 3/√13

cos Ф= adj/hypo = 2/√13

4 sinФ - 3 cosФ =

4 x 3/√13 - 3 x 2/√13

12/√13 - 6/√13= 6/√13

2 sinФ + 6 cosФ=

2 x 3/√13 + 6 x 2/√13

6/√13 + 12/√13= 18/√13

Now,

6/√13/18/√13 =

6/18= 1/3

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