3. Show 7sin^2θ +sinθcosθ = 6 is the same as tan^2θ + tanθ - 6 = 0

Start at answer: Use identity tanθ = sinθ/cosθ ; tan^2θ + tanθ - 6 = 0 is same as sin^2θ / cos^2θ + sinθ/cosθ - 6 = 0

Now remove denominators: sin^2θ + sinθcosθ - 6cosθ = 0

We use identity sin^2θ + cos^2θ ≡ 1 and rearrange to cos^2θ ≡ 1- sinθ and plug in : sin^2θ + sinθcosθ - 6(1-sin^2θ)

Same as: sin^2θ + sinθcosθ - 6 + 6sin^2θ = 0 , collect together for: 7sin^2θ+sinθcosθ-6=0

Same as: 7sin^2θ +sinθcosθ = 6

	Criado por Doc Boff quase 8 anos atrás

Trigonometric Problems