Question

Solve Tangent (x minus pi) minus cosine (x minus StartFraction 3 pi Over 2 EndFraction) = 0, x is an element of left-brace 0, 2 pi).

Answer 1

B

Explanation:

Answer 2

x ∈ {0, π, 2π}

Explanation:

The expression can be simplified, which facilitates an answer.

tan(x -π) -cos(x -3π/2) = 0

The tangent function has a period of π, so tan(x-π) = tan(x). The cosine function shifted right by 3π/2 is equivalent to the opposite of the sine function.

tan(x) +sin(x) = 0 . . . . substitute simpler equivalents

sin(x)/cos(x) +sin(x) = 0 . . . . use equivalent for tan(x)

sin(x)(1/cos(x) +1) = 0 . . . . factor out sin(x)

sin(x)(cos(x)+1)/cos(x) . . . . . combine terms to a single fraction

This has solutions where sin(x) = 0 and where cos(x) = -1. Those solutions are integer multiples of π.

x ∈ {0, π, 2π}