(c) sin^2(x)

calculations

cos^2(x)(sec^2(x)-1)

sec^2(x) = tan^2(x) + 1 can be written as tan^2(x)= sec^2(x)-1

so the final equation is written as cos^2(x)tan^2(x)

using the trigonometric equation tan x = sinx / cos x

we get sin x = tan x * cos x

hence the answer (c). sin^2 (x)

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