Verify each trigonometric identity

Question

tan²x(csc²x)-tan²x=1

Answer 1

sin^2 1 sin^2

-------- * -------- - ------------- = <---- rewritten using only sines and cosines

cos^2 sin^2 cos^2

sin^2 - sin^4

------------------ <--- common denominator

cos^2 sin^2

1 - sin^2

------------ <--- common factor of sin^2 cancels

cos^2

cos^2

------- <---- trig identity sin^2 cos^2 = 1

cos^2

= 1