SOLUTION: if 3 cot theta =2, find the value of 4 sin theta - 3 cos theta divided by 2 sin theta + 6 cos theta

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Question 888933: if 3 cot theta =2, find the value of 4 sin theta - 3 cos theta divided by 2 sin theta + 6 cos theta
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
3%2Acot%28theta%29=2
cot%28theta%29=2%2F3
cos%28theta%29%2Fsin%28theta%29=2%2F3
cos%28theta%29=%282%2F3%29sin%28theta%29
cos%5E2%28theta%29=%284%2F9%29sin%5E2%28theta%29
but
cos%5E2%28theta%29%2Bsin%5E2%28theta%29=1
Substituting,
%284%2F9%29sin%5E2%28theta%29%2Bsin%5E2%28theta%29=1
%2813%2F9%29sin%5E2%28theta%29=1
sin%5E2%28theta%29=9%2F13
sin%28theta%29=3%2Fsqrt%2813%29
cos%28theta%29=2%2Fsqrt%2813%29
So then,


and
%284sin%28theta%29-3cos%28theta%29%29%2F%282sin%28theta%29%2B6cos%28theta%29%29=6%2F18
%284sin%28theta%29-3cos%28theta%29%29%2F%282sin%28theta%29%2B6cos%28theta%29%29=1%2F3