The equation tan^2 x+1=sec^2 x is an identity true or false

Question

The equation tan^2 x+1=sec^2 x is an identity true or false

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Charlie 1 week 2021-09-11T02:18:33+00:00 1 Answer 0

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    2021-09-11T02:19:41+00:00

    Answer:

    tan²x + 1 = sec²x is identity

    Step-by-step explanation:

    * Lets explain how to find this identity

    ∵ sin²x + cos²x = 1 ⇒ identity

    – Divide both sides by cos²x

    ∵ sin x ÷ cos x = tan x

    ∴ sin²x ÷ cos²x = tan²x

    – Lets find the second term

    ∵ cos²x ÷ cos²x = 1

    – Remember that the inverse of cos x is sec x

    ∵ sec x = 1/cos x

    ∴ sec²x = 1/cos²x

    – Lets write the equation

    ∴ tan²x + 1 = 1/cos²x

    ∵ 1/cos²x = sec²x

    ∴ than²x + 1 = sec²x

    – So we use the first identity sin²x + cos²x = 1 to prove that

     tan²x + 1 = sec²x

    ∴ tan²x + 1 = sec²x is identity

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