buktikan identitas berikut [tex]1. cos ^{4} \alpha (1+tan ^{4} \alpha ) = 1-2 sin ^{2} \alpha cos \alpha ^{2} [/tex]

[tex]1.cos ^{4} \alpha (1 + tan ^{4} \alpha )[/tex]
= [tex]cos ^{4} \alpha + cos ^{4} \alpha . tan ^{4} \alpha [/tex]
= [tex]cos ^{4} \alpha + cos ^{4} \alpha( \frac{sin ^{4} \alpha }{cos ^{4} \alpha } )[/tex]
= [tex]cos ^{4} \alpha + sin ^{4} \alpha [/tex]
= [tex](cos ^{2} \alpha .cos ^{2} \alpha ) + (sin ^{2} \alpha . sin ^{2} \alpha )[/tex]
= [tex][cos ^{2} \alpha (1 - sin ^{2} \alpha )] + [sin ^{2} \alpha (1 - cos ^{2} \alpha )][/tex]
= [tex]cos ^{2} \alpha - sin ^{2} \alpha .cos ^{2} \alpha + sin ^{2} \alpha - cos ^{2} \alpha.sin ^{2} \alpha [/tex]
= [tex]1 - 2cos ^{2} \alpha .sin ^{2} \alpha [/tex]

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