5+4 tan^2 x = 1+4 sec ^2 x

IdenTitas TrigoNometRi

5 + 4 tan² x
= 5 + 4(sec² x - 1)
= 1 + 4sec² x
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5+4 tan^2 x = 1+4 sec ^2 x
Pembuktian trigonometri
5+4 tan^2 x harus sama nilai dgn 1+4 sec ^2 x

Ingat Sifat trigonometri
tan^2 x = sin^2 x / cos^2 x
Sin^2x = 1-cos^2x
Sec^2 x = 1/ cos^2 x

5+4 tan^2 x = 5+4( sin^2 x / cos^2 x)
= 5+4( (1-cos^2x) / cos^2 x))
= 5 +4 / cos^2 x -4
=1+ 4 / cos^2 x
=1+ 4 sec^2x
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