Question

Segitiga pqr dengan sudut p = 120° , qr = 12 cm , jika pq = 4√3 cm. Maka tentukan cos R!

Buktikan bahwa sin x/1+cos x + 1+cos x/sin x = 2 cosec x

Answer 1

Qr/ sin p = pq / sin r
12 / sin 120 = 4√3 / sin r
12 sin r = 4√3 sin 120
12 sin r = 4√3 x (1/2)√3
12 sin r = 6
sin r = 1/2
sin² r + cos² r = 1
(1/2)² + cos² r = 1
1/4 + cos ² r = 1
cos²r = 1 - 1/4
cos² r = 3/4
cos r =  + (1/2)√3

sin x / (1 + cos x) + (1+cos x) /sin x
= (sin² x + (1 + cos x)² ) / sin( 1 + cos x)
= (sin ² x + 1 + 2 cos x + cos²x) / sin (1 + cosx)
= (sin² x + cos² x + 1 + 2 cos x) / sin (1 + cos x)
= (1 + 1 + 2cos x) / sin (1 + cos x)
= (2 + 2 cos x) / sin (1 + cos x)
= 2 (1 + cos x) / sin (1 + cos x)
= 2 / sin x
= 2 cosec x  (terbukti)