Trigonometry
posted by Jasmine .
How do you verify the equation is an identity?
Tan^2xtan^2y=sec^2xsec^2y
and, how do you factor and simplify,
cscx(sin^2x+cos^2xtanx)/sinx+cosx

One of the basic identities is
tan^2 A + 1 = sec^2 A which gives Tan^2 A = sec^2 A  1
so
Left side
= tan^2xtan^2y
= sec^2x  1 (sec^2y  1)
= sec^2x  sec^2y
= Right Side 
For the second, I will assume you meant
cscx(sin^2x+cos^2xtanx)/(sinx+cosx)
= 1/sinx(sin^2x + cos^2xsinx/cosx)/(sinx + cosx)
= 1/sinx(sin^2x + sinxcosx)/(sinx+cosx)
= (sinx + cosx)/sinx + cosx)
= 1