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Establish the identity: 1/1 - sin x = secsquared x + tan x sec x?

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my math is rusty, could really use some help.

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  1. Multiply above and below by (1+sin x)

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

    = 1/cos^2 x + (sin x/cos x)(1/cos x)

    = sec^2 x + tan x sec x

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