Prove that
1 / cos(x) − cos(x) = sin(x) ∙ tan(x) for x ≠ + k, for all integers k.

 From the given expression we can get the  fundamental trigonometry identity

Step-by-step explanation:

1 ÷ cos (×) - cos (×) = sin (×) * tan (×)  ⇒

[1 ÷ cos (×) ] - cos (×) = sin (×)* sin(×)/ cos (×)

1/ cos(×) - cos (×) = sin²(×)/cos(×) ⇒cos(×)/cos(×) -cos²(×) = sin²(×)

1 - cos²(×) = sin²(×)

1= cos²(×) + sin²(×)     fundamental trigonometry identity

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation: