Cos 3x*cos X + Sin 3x*sin X=

cos 3x*cos x + sin 3x*sin x=

= cos (3x-x)
= cos 2x jikalau soal opsi mampu pula jawaban lain ialah :
                  = cos²x – sin²x
                  = 2 cos²x -1
                   = 1- 2 sin²x

sin 3x – sin x / cos x – cos 3x

(sin 3x – sin x)/(cos x – cos 3x)
= 2 cos 2x . sin x)/ (- 2 sin (-2x). sin (-x))
= ( 2 cos 2x . sin x)/(-2(-1)(-1) . sin 2x sin x)
= (2 cos 2x  sin x) / (-2 sin 2x sin x)
= – cos 2x/sin 2x
= – cot 2x

sin 3x – sin x / cos x – cos 3x

Mapel : Matematika
Bab : Trigonometri

RUMUS
[tex]\boxed \sin a – \sin b = 2 \cos( \frac a + b 2 ) \sin( \frac a – b 2 ) [/tex]
[tex]\boxed \cos a – \cos b = – 2 \sin( \frac a + b 2 ) \sin( \frac a – b 2 ) [/tex]

[tex] \sin 3x – \sin x \\ = 2 \cos( \frac 3x+ x 2 ) \sin( \frac 3x – x 2 ) \\ = 2 \cos( \frac 4x 2 ) \sin( \frac 2x 2 ) \\ = 2 \cos( 2x ) \sin( x )[/tex]
[tex] \cos x – \cos 3x \\ = – 2 \sin( \frac x + 3x 2 ) \sin( \frac x – 3x 2 ) \\ = – 2 \sin( \frac 4x 2 ) \sin( \frac – 2x 2 ) \\ = – 2 \sin(2x ) \sin( – x ) \\ = 2 \sin(2x ) \sin( x )[/tex]
sin 3x – sin x / cos x – cos 3x
[tex] = \frac 2 \cos( 2x ) \sin( x ) 2 \sin(2x ) \sin( x ) \\ = \frac \cos(2x) \sin(2x) \\ = \cot(2x) [/tex]
Semoga menolong

cos 3x . cos x + sin 3x . sin x =

cos (3x-x)…………….

sin 3x/sin x + cos 3x/cos x

Trigonometri

bentuk sederhana dari
(sin 3x)/ sinx  + (cos 3x)  cos x =
= (sin 3x cos x + cos 3x  sin x) / (sin x cos x)
= sin (3x +  x)/ 1/2 (2 sin x cos x)
= sin 4x / 1/2 sin 2x
= 2 sin 4x/ sin 2x
= 2 (2 sin 2x cos 2x) / sin 2x
= 4 sin 2x cos 2x / sin 2x
= 4 cos 2x
,,