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rosie
rosie asked in Science & MathematicsMathematics · 6 months ago

Trigonometric identity question help?

(cos^4θ-sin^4θ)/cos^2θ = 1-tan^2θ

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

3 Answers

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  • Ian H
    Lv 7
    6 months ago

    (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
    Lv 7
    6 months ago

    (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
    Lv 7
    6 months ago

    (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

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