How do you prove this is an identity?

sec x sin x +cscx cos x = tan x + cot x

Verify the following identity:

sec(x) sin(x) + csc(x) cos(x) = tan(x) + cot(x)

Write cotangent as cosine/sine, cosecant as 1/sine, secant as 1/cosine and tangent as sine/cosine:

1/cos(x) sin(x) + 1/sin(x) cos(x) = ^?cos(x)/sin(x) + sin(x)/cos(x)

Put cos(x)/sin(x) + sin(x)/cos(x) over the common denominator sin(x) cos(x): cos(x)/sin(x) + sin(x)/cos(x) = (cos(x)^2 + sin(x)^2)/(cos(x) sin(x)):

(cos(x)^2 + sin(x)^2)/(cos(x) sin(x)) = ^?cos(x)/sin(x) + sin(x)/cos(x)

Put cos(x)/sin(x) + sin(x)/cos(x) over the common denominator sin(x) cos(x): cos(x)/sin(x) + sin(x)/cos(x) = (cos(x)^2 + sin(x)^2)/(cos(x) sin(x)):

((cos(x)^2 + sin(x)^2)/sin(x))/cos(x) = ^?(cos(x)^2 + sin(x)^2)/(cos(x) sin(x))

The left hand side and right hand side are identical:

(identity has been verified)

Step-by-step explanation:

Hey!

Step 1:

You want to find how many calories are in one pretzel.

192 / 12 = 16

So there are 16 calories in each pretzel.

Step 2:

Multiply 16 to 15 to find how many calories are in 15 pretzels.

16 x 15 = 240

You will consume 240 calories if you eat 15 pretzels.

Hope This Helped! Good Luck!