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3a)

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The trigonometric function is sec x / tan x .

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Rewrite sec x = ( 1 / cos x )  and tan x  = ( sin x / cos x ) .

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Cancel common terms .

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3b)

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The trigonometric function is (sec x – 1)(sec x + 1) .

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The above expression is in the form of  (a+b)(a-b) = a2 - b2 .

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(sec x – 1)(sec x + 1) = sec2 x  - 12 .

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(sec x – 1)(sec x + 1) = sec2 x  - 1 .

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We know the trigonometric identity sec2 x  - 1 = tan2 x .

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Therefore (sec x – 1)(sec x + 1) = tan2 x .

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3c)

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The trigonometric function is (sin x)(sec x) .

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Rewrite sec x = ( 1 / cos x ) .

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We know the trigonometric identity  ( sin x / cos x ) = tan x  .

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