Jika cos^2 a = 3/5 tentukan cos 2a, sin 2a dan tan 2a

cos^2 a = 3/5 tentukan cos 2a, sin 2a dan tan 2a

Rumus identitas
cos^2 a +sin ^2 a =1
sin ^2 a =1 -cos ^2 a

cos^2 a = 3/5 => sin ^2 a =1-3/5=2/5
Cos a = √3/5 => sin a = √2/5
Tan a= sin a / cos a = √2/3

cos 2a
= cos^2 a -sin ^2
=3/5-2/5=1/5

sin 2a = 2× sin a ×cos a
= 2×√2/5×√3/5
= 2×√6/25
= 2/5 √6

tan 2a
= 2×tan a / 1- tan^2a
=(2 ×√2/3 ) / 1- 2/3
=(2 ×√2/3 ) / 1/3
=2 ×√2/3 ) ×3/1
=6 ×√2/3