Question

Verify the following statement: (1)/(sinx)-(1)/(cosx)=(cosx-sinx)/(sinxcosx)

Answer 1

Sure, let's verify the following mathematical statement step by step:

1/sin(x) - 1/cos(x) = (cos(x) - sin(x)) / (sin(x)cos(x))

Step 1:

First, find common denominators on the left side of the equation which are sin(x) and cos(x).
To do that we need to multiply the first term by cos(x)/cos(x) and the second term by sin(x)/sin(x):

(cos(x)/sin(x)cos(x)) - (sin(x)/sin(x)cos(x))

Step 2:

Now you can combine the two fractions as they have the same denominator:

(cos(x) - sin(x)) / (sin(x)cos(x))

So, the given mathematical statement is true:

1/sin(x) - 1/cos(x) = (cos(x) - sin(x)) / (sin(x)cos(x))

and we have our proof done!