Which of the following expressions can be simplified such that the result is equal to 1?
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Correct Answer: D. cos x (tan x * sin x + cos x)
This problem is solved through the use of trigonometric identities. It should be known that sin2x + cos2x = 1. Thus, we are looking for an answer that simplifies to that identity. Answers A and E are not correct because the square of the sum of sin x +/- cos x results in a sin x * cos x term. Thus, although they may seem initially correct, multiplying out the equation shows that it is not. In answer D, we first see that tan x = sinx/cosx. Thus, cosx * tanx = sinx, and cosx * tanx *sinx = sin2x. Thus, multiplying through the equation, we come to the correct identity of sin2x + cos2x = 1.
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