Posted by Jasmine on Sunday, January 3, 2010 at 12:39pm.
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^2x-tan^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
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