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8 June, 04:11

Match the right side of the equation to the left side

cot x sec^4 x=cot x + 2 tan x+tan^3 x

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  1. 8 June, 05:59
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    Step-by-step explanation:

    cot x + 2 tan x + tan³ x

    Write in terms of sine and cosine:

    (cos x / sin x) + 2 (sin x / cos x) + (sin³ x / cos³ x)

    Find the common denominator:

    (cos⁴ x / (sin x cos³ x) + 2 (sin² x cos² x / (sin x cos³ x)) + (sin⁴ x / (sin x cos³ x))

    Add:

    (cos⁴ x + 2 sin² x cos² x + sin⁴ x) / (sin x cos³ x)

    Factor:

    (sin² x + cos² x) ² / (sin x cos³ x)

    Pythagorean identity:

    1 / (sin x cos³ x)

    Multiply top and bottom by cos x:

    cos x / (sin x cos⁴ x)

    Simplify:

    cot x sec⁴ x
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