Question

Verify the identity tan x + cot x =csc x× sec x

Answer 1

tan(x) + cot(x) can be expressed as the following:


`(sin(x))/(cos(x)) + (cos(x))/(sin(x))`

Find the common denominator:


`(sin^2(x)+cos^2(x))/(sin(x)cos(x))`

We can use a Pythagorean identity to replace
`sin^2(x) + cos^2(x)` with 1.

So now we have
`(1)/(sin(x)cos(x))` or
`(1)/(sin(x)) * (1)/(cos(x))`

Which equals:


`csc(x)sec(x)`