Trigonometric identity question help?

Question

(cos^4θ-sin^4θ)/cos^2θ = 1-tan^2θ

Can someone show me step by step how to solve this please?

Ian H · Answer

(c^4 - s^4)/c^2 = 1 - t^2 multiply both sides by c^2
(c^2 - s^2)(c^2 + s^2) = (c^2 - s^2)
That is true because c^2 + s^2 = 1

stanschim · Answer

(cos(θ))^4 - (sin(θ))^4 / (cos(θ))^2

[((cos(θ))^2)^2 - (sin(θ))^4] / (cos(θ))^2

[((1 - (sin(θ))^2))^2 -  (sin(θ))^4] / (cos(θ))^2

[1 - 2(sin(θ))^2 + (sin(θ))^4 - (sin(θ))^4] / (cos(θ))^2

[1 - 2(sin(θ))^2] / (cos(θ))^2

[1 - (sin(θ))^2 - (sin(θ))^2] / (cos(θ))^2

[(cos(θ))^2 - (sin(θ))^2] / (cos(θ))^2

1 - (tan(θ))^2

Robert · Answer

(cos^4 𝚹 - sin^4 𝚹) / cos^2 𝚹 =

(cos^2 𝚹 + sin^2 𝚹)(cos^2 𝚹 - sin^2 𝚹) / cos^2 𝚹 =

(cos^2 𝚹 - sin^2 𝚹) / cos^2 𝚹 =

1 - tan^2 𝚹