Question

IF cot = 5/12
find 5 sin - 3 cos/5 sin+3 cos
please mention steps

Answer 1

Step-by-step explanation:

cot theta=adj/opp=5/12

hyp²=opp²+adj²

hyp²=12²+5²

hyp²=144+25=169

hyp=√169=13

sin theta=opp/hyp=12/13

cos theta=adj/hyp=5/13

(5 sin theta-3 cos theta)/(5sin theta+3 cos theta)

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

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

(45/13)/(75/13)

45/75

3/5