Question

if 5 sin θ -12cos θ=0, then find the value of tan θ and cos θ

help fast please!!!​

Answer 1

5 cosθ – 12 sin θ = 0

⇒5 cos θ = 12 sinθ

⇒sinθ/cosθ = 5/12

⇒tanθ = 5/12

As we know,

Hypotenuse = H, Perpendicular = P and Base = B

tan θ = P/B = 5/12

As we know,

H2 = P2 + B2

⇒H2 = 122 + 52 = 144 + 25 = 169

⇒H = √169 = 13 cm

sinθ = P/H = 5/13 and cos θ = B/H = 12/13

Now,

(1 + sinθ + cos θ)/(1 – sinθ + cosθ)

⇒(1 + 5/13 + 12/13)/(1 – 5/13 + 12/13)

⇒(13 + 12 + 5)/(13 – 5 + 12)

⇒30/20

⇒3/2

hope it's helpful to you