cos x ∗ cos 2 x + 2 cos x ( s in 2 x ) 2 = cos x cos x ∗ ( co s 2 x − s i n 2 x ) + 2 cos x ( 2 s in x cos x ) 2 = cos x cos x ∗ ( co s 2 x − s i n 2 x ) + 2 cos x 4 s i n 2 x co s 2 x = cos x cos x ∗ ( co s 2 x − s i n 2 x ) + 2 s i n 2 x cos x = cos x ∣ D i v i d e b y cos x ( co s 2 x − s i n 2 x ) + 2 s i n 2 x = 1 co s 2 x − s i n 2 x + 2 s i n 2 x = 1 co s 2 x + s i n 2 x = 1 1 = 1 TR U E
cos x cos 2 x + 2 cos x s i n 2 2 x = cos x L = cos x ( co s 2 x − s i n 2 x ) + 2 cos x ( 2 s in x cos x ) 2 = co s 3 x − s i n 2 x cos x + 2 cos x ( 2 s in x cos x ) 2 = 2 cos x ( co s 3 x − s i n 2 x cos x ) + ( 2 s in x cos x ) 2 = 2 cos x 2 co s 4 x − 2 s i n 2 x co s 2 x + 4 s i n 2 x co s 2 x = 2 cos x 2 co s 2 x ( co s 2 x + s i n 2 x ) = cos x u se : s i n 2 x + co s 2 x = 1 ( s i n 2 x + co s 2 x ) = cos x = R \center L = R
Ot h er t h eore m s : s in 2 x = 2 s in x cos x cos 2 x = co s 2 x − s i n 2 x
We proved that cos x ⋅ cos 2 x + 2 c o s x ( s i n 2 x ) 2 = cos x by simplifying both sides using trigonometric identities and factoring. The process demonstrated that both sides are indeed equal, confirming the identity. Thus, the equation is valid for all values of x where cos x is defined.
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Jawaban:(Bahasa Gorontalo)Perisai = Tabu atau Pajango