Show that y/X^2√4+X^2=CSCøCOTø (when x=2tanø and Y= 2sec^2ø)?

Question

Show that y/X^2√4+X^2=CSCøCOTø (when x=2tanø and Y= 2sec^2ø)

4+X^2 is all under the root symbol "√"

Answer 1

Ok, the equation is :

y / ( x^2*sqrt( 4+x^2 ) = CSCøCOTø

x = 2tanø

y = 2sec^2ø

replacing those values :

2sec^2ø / 4tan^2ø*sqrt( 4 + 4tan^2ø)

2sec^2ø / 4tan^2ø*2sqrt(1 + tan^2ø)

1 + tan^2ø = sec^2ø

2sec^2ø / 4tan^2ø*2secø

secø / tan^2ø = (1/cosø)(sin^2ø / cos^2ø) = cosø / sin^2ø

that's equal to : Cotø*Cscø

because : 1/sinø = cscø and cosø / sinø = cotø

So that's it man.

Hope that helped you