Simplify tan^4x + 2tan^2x + 1?

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work please, how did you get that?

4 Answers

  • There’s a trig identity that states:

    1+tan^2 x=sec^2 x

    We want to find what tan^2 x equals. To do this, subtract 1 from both sides.

    tan^2 x=sec^2x-1

    Now plug it into your expression:

    (tan^4 x)+2(tan^2 x)+1=

    (tan^2 x)(tan^2 x)+2(tan^2 x)+1

    (sec^2 x-1)(sec^2 x-1)+2(sec^2 x-1)+1

    (sec^4 x)-2(sec^2 x)+1+2(sec^2 x-1+1

    sec^4 x

  • tan^4(x) + 2tan^2(x) + 1 = (tan^2(x) + 1)^2 = (sec^2(x))^2 = sec^4(x)

  • tan^4x + 2tan^2x + 1

    = (tan^2x + 1)^2

    = (sec^2x)^2

    = sec^4x

  • sec^4 (x)

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