What basic trigonometric identity would you use to verify that sin x +1/ sin x=1 +csc x
a. sinx=cos x tan x
b. cos^2 x+ sin^2 x=1
c. csc x=1/ sin
d.1+cot^2x=csc^2x

 The correct option is (c).

Step-by-step explanation:  We are given to select the correct basic identity that we will use to verify the following:

We have

In order to verify the given trigonometric equation, we must have

Thus, the required identity that we will use is

Option (c) is CORRECT.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is