Question

If 5 . sin – 12. cos = 0 Find the value ​

Answer 1

5cosθ−12sinθ=0

⇒5cosθ=12sinθ

⇒cotθ=

5

12

⇒

2cosθ−sinθ

sinθ+cosθ

=

sinθ(2cotθ−1)

sinθ(1+cotθ)

=

2×

5

12

−1

1+

5

12

=

5

24

−1

5

17

=

5

24−5

5

17

=

5

17

×

19

5

=

19

17

Hence, the answer is

19

17

.

Answer 2

Answer: $\frac{sin + cos}{sin - cos}$ = $\frac{17}{7}$

Step-by-step explanation:

5sinθ - 12cosθ = 0

5sinθ = 12cosθ

sinθ/cosθ = 12/5

tanθ=12/5

opp/adj = 12/5

a² + b² = c² (Pythagoras)

12² + 5² = c²

144 + 25 = c²

c² = 169

c = 13

opp = 12    adj = 5   hypo = 13

sinθ = 12/13    cosθ= 5/13

sinθ+cosθ = 12/13 + 5/13 = 17/13

sinθ - cosθ = 12/13 - 5/13 = 7/13

$\frac{sin + cos}{sin - cos}$= $\frac{\frac{17}{13} }{\frac{7}{13} }$

$\frac{sin + cos}{sin - cos}$ = $\frac{17}{7}$