Question

Show that the equation is not an identity by finding a value of x for which both sides are defined but not equal. cos x - cos x sinx = cos^3 x

A. π
B. 0
C. π/4
D. π/2

Answer 1

start by dividing each term by cos(x)

1 - sin(x) = cos^2(x)

and cos^2(x) = 1 - sin^2 (x) from the trig identity sin^2 + cos^2 = 1

so you have

1 - sin(x) = 1 - sin^2(x)

or

sin^2(x) - sin(x) = 0

solve for x by factorising the quadratic equation.