got 20 (14 complete) Shew that the functons fand o are identically equal Rewrite

Question

got 20 (14 complete) Shew that the functons fand o are identically equal Rewrite the espression for f(x) by applying a quotient identity and simplftying. Do not apply any trigonometric identy sincotx "€ (Simplify your answer.) Rewrite the expression from the previous step, applying a Pythagorean Identity to the numerator The faction tom the previous step may be rewrtten as sec x cos x using what? Select all that apply A. Quotient Identity B. Pythagorean Identity D. Ever-Odd identity C. Cancellation Property E. Reciprocal Identity

Explanation / Answer

f(x) = sin x * 1/ cot x

sin x * 1/ cot x = sin x * tan x

tan x = sin x / cosx

sin x * 1/ cot x = sin^2 x / cos x

now applying pythagorean identity on numerator

sin^2x = ( 1- cos^2 x )

= ( 1 - cos^2 x ) / cos x

now this step can be rewritten as

1/ cos x - cos^2 x / cos x = sec x - cos x

1/ cos x = sec x ( reciprocal identity )

cos^2 x / cos x = cos x ( cancellation property )

so two properties used are   reciprocal identity and  cancellation property

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