Use trigonometric identities to simplify the following expressions:
a) cos²θ(1+tan²θ)
b) tan²θ-sec²θ+sin²θ+cos²θ
a) cos2(x) · ( 1 + tan2(x) ) = cos2(x) + cos2(x) ·tan2(x) = cos2(x) + cos2(x) · sin2(x) / cos2(x)
= cos2(x) + sin2(x) = 1
b) tan2(x) - sec2(x) + sin2(x) + cos2(x) = tan2(x) - sec2(x) = tan2(x) - [ 1 + tan2(x) ]
= tan2(x) - 1 - tan2(x)
= -1
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