BAB TRIGONOMETRI kelas 11​

Jawab:

trigonometri

rumus jumlah dan perkalian

cos (A + B) = cos A cos B – sin A sin B

Penjelasan dengan langkah-langkah:

i) cos (22,5 -a ) cos (22,5 + a)  - sin (22,5 -a )(sin 22,5 + a) =

A= 22,5 + a dan B =  22,5 – a

cos B cosA  - sin B sin A = cos (A + B)

= cos (22,5 -a + 22,5 + a)

= cos 45

= 1/2 √2

2)  cos (π/2 +a) cos (π/6 +a) – sin (π/2 +a) sin (π/6 +a) =

= – sin a  cos (π/6 +a) – cos a sin (π/6 +a)

= – (sin a  cos (π/6 +a) + cos a sin (π/6 +a))

= – sin (a + π/6 +a)

= – sin (2a+ π/6)

= – { sin 2a cos π/6+ cos 2a  sin π/6)

= – { sin2a (1/2√3 ) + cos 2a ( 1/2)}

= – 1/2 (√3 sin 2a +  cos 2a)

a]

cos (x + y) = cos x cos y – sin x sin y

soal tulis kembali

= cos (22,5 – a + 22,5 + a)°

= cos 45°

= 1/2 √2

b]

soal

= cos (π/2 + a + π/6 + a)

= cos (2a + 90° + 30°)

= cos (2a + 120°)

= cos 2a cos 120° – sin 2a sin 120°

= cos 2a . (-1/2) – sin 2a . (1/2 √3)

= -1/2 (cos 2a + √3 sin 2a)