Tugas Kelas XI-IA 5,XI-IA 6, XI-IA 7

Submit your work at friday, November, 5th

1. Prove the following identities :
a. ( sin x - sin 2x + sin 3x ) / ( cos x - cos 2x + cos 3x ) = tan 2x
b. cos 3p + sin 3p = ( 1 + 2 sin 2p )( cos p - sin p )
c. 2 tan 2c = ( tan 2c - sin 2c )( cosec^2 c)
d. sin p. cos 2p. sin 3p = 0.25 ( 1 - cos 2p + cos 4p - cos 6p)
e. sin k + sin 2k + sin 3k = 2 sin k cos k ( 2 cos k + 1 )
f. In a triangle PQR, sin 2P + sin 2Q + sin 2R = 4 sinP sinQ sin R
g. In a triangle ABC, sinB sinC sin(B-C) + sinC sinA sin(C-A)
+ sinA sinB sin(A-B) = - sin(B-C) sin(C-A) sin(A-B)

2. Solve the following equations for the angles between 0 to 2 phi radians.
a. cos 5x - cos x = sin 3x
b. sin 2x - sin 4x + sin 6x = 0
c. cos 3x - sin 3x = 2 sinx + cos x

3. Given that sin x = m + n and cos x = m - n.
a. show that m^2 - n^2 = 0.5 sin 2x
b. express m/n in terms of tan x. Hence find the value of tan x if m = 3n.

Do your best, wishes that you can get more advantages from this task.