Asked by Nami
Which of the following counterexamples proves that sinxtanx=cosx is not a trigonometric identity? Select all that apply.
-2π
-3π
-3π/4
-π/4
Answers
Answered by
Reiny
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.
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.