Prove the following identity.
tan²θcos²θ+cot²θsin²θ=1
tan2(x)·cos2(x) + cot2(x)·sin2(x)
= [ sin2(x) / cos2(x) ] · cos2(x) + [ cos2(x) / sin2(x) ] · sin2(x)
= [ sin2(x) / cos2(x) · cos2(x) ] + [ cos2(x) / sin2(x) · sin2(x) ]
= sin2(x) + cos2(x)
= 1