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A. cos x b. tan x c. sec x d. cot x Simplify the expression

A. cos x b. tan x c. sec x d. cot x Simplify the expression-example-1
User NaviRamyle
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1 Answer

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First, multiply by 1:

cos x * 1 + cos x tan^2 x

Factor cos x out of cos x tan^2 x

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

Factor again

cos x (1+ tan^2 x)

Rearrange:

cos x (tan^2 x +1 )

Apply Pythagorean identity:

cos x * sec ^2 x

Rewrite Sec x in terms of sin and cos

cos x * (1 / cos x )^2

Apply product rule:

cos x * 1^2 / cos^2 x

cos x * (1/ cos^2 x )

Cancel common factor cos x

1 / cos x

1/cosx = sec x

Answer : sec x (option c)

User Ten Sleep
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