If cos⁴A+cos²A=1,prove that tan⁴A+tan²A=1​

Question

If cos⁴A+cos²A=1,prove that tan⁴A+tan²A=1​

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Brielle 1 month 2021-09-16T16:53:51+00:00 2 Answers 0 views 0

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    0
    2021-09-16T16:55:25+00:00

    Answer:

    tan⁴A +tan²A=1

    then show that cos⁴ A+cos²A=1

    ANSWER :

    Here

    tan⁴A+tan²A=1

    tan⁴A=1-tan²A

    tan⁴A=sec²A

    sin⁴A/cos⁴A =1/cos²A

    sin⁴A=cos²A

    so by taking square root on both the sides

    √sin⁴A=√cos²A

    sin²A=cosA……..1

    now

    LHS

    =cos⁴A +cos²A

    sin²A+cos²A…..from 1

    =1

    =RHS

    identity used :

    sin²A+cos²A=1

    tanA=sinA/cosA

    1+tan²A=sec²A

    0
    2021-09-16T16:55:42+00:00

    hope this helps u

    QUESTION :

    tan⁴A +tan²A=1

    then show that cos⁴ A+cos²A=1

    ANSWER :

    Here

    tan⁴A+tan²A=1

    tan⁴A=1-tan²A

    tan⁴A=sec²A

    sin⁴A/cos⁴A =1/cos²A

    sin⁴A=cos²A

    so by taking square root on both the sides

    √sin⁴A=√cos²A

    sin²A=cosA……..1

    now

    LHS

    =cos⁴A +cos²A

    sin²A+cos²A…..from 1

    =1

    =RHS

    identity used :

    sin²A+cos²A=1

    tanA=sinA/cosA

    1+tan²A=sec²A

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