Csc X/ (cot X + Tan X) = Cos X How Do I Verify?

Csc(x) / [cot(x) + tan(x)] = because(x)

Take the left hand side
= csc(x) / [cot(x) + tan(x)]

Convert to sines and cosines.

= [1/sin(x)] / [(because(x)/sin(x)) + (sin(x)/because(x))]

Now, multiply and divide by sin(x)because(x).
= (( sin(x)because(x)) * [1/sin(x)]) / ((
sin(x)because(x)) * [(because(x)/sin(x)) + (sin(x)/because(x))])

you will get

= [because(x)] / [because^2(x) + sin^2(x)]

Note that because^2(x) + sin^2(x) =1, therefore



LHS = because(x) / 1

= because(x) which is equal to RHS