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  • 01-08-2019
  • Mathematics
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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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MathPhys
MathPhys MathPhys
  • 01-08-2019

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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