Which of the following counterexamples proves that sinxtanx=cosx is not a trigonometric identity? Select all that apply.

Question

-2π
-3π
-3π/4
-π/4

Answer 1

method1:
simply substitute each value into the equation to each if
it satisfies.
If the given value satisfies the equation, it clearly cannot be
used as a counter-example.
If the given value does not satisfy the equation ........

method 2: actually solve the given equation to see which
values are solutions.
sinxtanx = cosx
sinx(sinx/cos) = cosx
sin^2 x = cos^2 x
cos^2 x - sin^2 x = 0
cos(2x) = 0

2x = ± π/2 , ± because of the symmetry of the cosine curve in the y-axis

x = ± π/4
since cos 2x has a period of π
+π/4 - π = -3π/4 is also solution

Clearly since -π/4 and -3π/4 are in your list and they satisfy
the equation they CANNOT be used as counterexamples.